Let's solve the elliptic curve formula! Is the key to using Fermat's little theorem effectively? dragon blog

Hello. This is Tenmei Watanabe from Dragon Blog. Last time and the day before last, we explained two keywords for mixing in this article. In other words, it's about linear congruences and Fermat's little theorem. Do you remember? about me. It's not a friend I haven't seen in a while, but I would like to check these two keywords again.

Now, the first-order congruence expression is ``a and b are congruent modulo m.'' I'm trying to confuse the reader right away, but the expression a ≡ b (mod m) means that the remainders when a and b are divided by m are the same. In a fantasy world, my confusion strategy is to use things like evening primrose to solve confusion, but next time I'll use Fermat's Little Theorem, which is even more difficult.

Fermat's little theorem is an impregnable cipher with the formula a^(p-1)≡1 (mod p), where if p is a prime number, then a has a value from 1 to p-1 and becomes 1 with mod p. is. This time, I would like to talk about elliptic curve cryptography, so please think of the keyword "cipher" as a foreshadowing.

If you remember the name Euler's phi function from last time, you should remember that the correct name is a^φ(p)= 1 mod p. I'll put a link to the previous article here. I generally don't like to read articles, so if you fall and have to call an ambulance, I'll immediately transport you to a fantasy world and teach you a spell that will help you walk without legs. Is it a ghost? ? It's a little surreal (lol).

Well, I'll leave the idle gag here for the first time in a while. φ(p) is the number of numbers for which p is relatively prime. In other words, if p is a prime number 7, then there are 7-1 = 6, and if p is a non-prime composite number 9, there are 6, 1, 2, 4, 5, 7, and 8. In this case, φ(7)=6 and φ(9)=6, respectively. In other words, if we multiply a six times and mod p, then if a and p are relatively prime, we get 1 mod p.

Well, I've explained it quite quickly and sloppily so far. This is a review, but if you want to know more, please refer to the previous and previous articles.

Now let's talk about codes. This is a story about the demon world called codes, so please continue to enjoy my story if you like.

When you think of codes, some people may think of the runes of ancient civilizations. From the point of view of modern people, the letters used in the distant past are truly worthy of the name cipher. Let's code! !

Among the codes that are often used in modern times, the codes that are commonly used in modern times are the RSA code, which involves decomposition of prime factors, and the elliptic curve code, which uses elliptic curves. RSA encryption, which is a prime factorization code, is used to send credit card pin numbers to the bank where you have your deposit account. On the other hand, what do you think about elliptic curves even if you ask an elderly person? It is used in codes related to cryptocurrencies, which may be said to be.

This time, I would like to introduce a method to easily find a solution for this elliptic curve. Hello everyone? Primary congruence? Fermat's little theorem? What was it? Instead, please try to prepare and review the previous article. If you do that, you should be able to see the beginning of my story.

Now, what is the elliptic curve cryptography used in Bitcoin? First, look at the following formula: This time, it is not meant to be multiplied by x, but expressed as a single variable. Be careful! !

y^2 ≡ x^3 + 7 mod p

Those who think that complicated surgical techniques should not be used. Please rest assured. Since the values ​​of y and p are known in advance, only x is found. By the way, the symbol "^" means y^2, which is the square of y. In other words, y is multiplied twice. x^3 is x to the third power. In other words, it means x multiplied three times.

For example, let's say y=11, p=17. Actually, if you substitute the numerical values ​​and organize them, you will get the following.

11^2 ≡ x^3 + 7 mod 17

121 – 7 ≡ x^3 mod17

x^3 ≡ 114 mod 17 ≡ 12 mod 17

x^3 ≡ 12 mod 17　

Here, the remainder when dividing 114 by 17 is 12. One of the points is that the equation of this elliptic curve is a cubic congruence. In other words, it is a congruence of x to the third power. Let's apply Fermat's little theorem to this. Let's raise both sides to the 5th power.

x^(3×5) ≡ 12^5 mod 17

Since p=17 is a prime number, x^16 is 1mod17 if x and p are relatively prime. Then multiply both sides by x.

x^(3×5+1) ≡ x(12^5) mod17

x^16 mod 17 ≡ 1mod17 ① 

 (12^5)x mod 17 ≡ 248832x mod17 ≡ 3x mod17 ②

3x mod 17 ≡ 1 mod 17 ②＝①

Multiplying both sides by 6 gives 18x, which becomes 17x+x ≡ x mod17. For information on how to find 6 multiplied by both sides, please refer to Euclid's mutual division method in the previous article.

x mod 17 ≡ 6 mod 17 　

Answer: x = 6 mod 17

Calculation: x^3 ≡ 6^3 ≡ 12 mod 17

Therefore, you know the answer. Let's take another example. What if y=8,p=17?

8^2 ≡ x^3 + 7 mod 17

64 – 7 ≡ x^3 mod17

x^3 ≡ 57 mod 17 ≡ 6 mod 17

x^3 ≡ 6 mod 17　

x^(3×5) ≡ 6^5 mod 17

x^(3×5+1) ≡ x(6^5) mod 17

x^16 ≡ 1 mod 17 ≡ (6^5)x mod 17 ≡ 7776x mod 17 ≡ 7x mod 17

7x ≡ 1 mod 17

Multiply both sides by 5.

35x ≡ x ≡ 5 mod 17

x ≡ 5 mod 17

x^3 ≡ 5^3 ≡ 6 mod 17　

So, I know the answer. The key point here is Fermat's little theorem. The key point is that depending on how you use Fermat's little theorem, a^(p-1) becomes 1 mod p. No matter how many a's are multiplied together, it can be converted to 1 mod p depending on the conditions.

This time we explained how to find the answer for an elliptic curve, but for example, it is also possible to find a, b, and c for a given value of p for a^3+b^3+c^3=p. maybe. Let's do the math on this one ourselves. The difficulty level is quite high. Let's make a legend meeting.

How was it. It seems that the linear congruence equation and Fermat's little theorem are closely related, but by synthesizing them, I was able to discover a new way to solve the mathematical equation. This time I just mixed two keywords, but you might be able to find a more advanced way of thinking if you mix three keywords. This time is over. See you soon. 

Are you confused about moving from the field to middle management? Communication is for managers!

 This is Watanabe, the blog owner. Watanabe is a field worker who loves the field. However, he may also become a middle manager from now on. If you are a middle manager or a reader, you must have been confused when you were first appointed to your position. So, I would like to write about what happened when I was promoted from the field to middle management.

table of contents

・Management IS communication! Skills are fundamentally different between managerial positions and those in the field.

・Watanabe meets anti-victim! ? 20% are allies, 60% are not interested and 20% are enemies! !

Management is communication! Skills are fundamentally different between managerial positions and those in the field.

　Middle management. Hmm. Starting a management career can be confusing at first . Up until now, I had been fulfilling my duties on-site, but now I am in a supervisory position, and my responsibilities have increased.

“After all, wouldn’t it be ideal for Watanabe to be ranked more like the second son of a 30-year-old boy than a middle manager?”

　I have brothers, but I don't have three brothers, so I admire having many brothers. However, when you have several subordinates who are like brothers, you have to keep track of everyone's situation at all times , which I think is difficult.

<Related articles>

• Is it necessary to go into detail? ? I get tired of roundabout explanations! ?
• Write in English with Google Translate! Junior high school level English proficiency is required, but easy English translation

　In the first place, management can be said to have a completely different nature from any previous job. After all, it is necessary to create a comfortable working environment, and communication is important . There is also the position of playing manager, in which case you will be responsible for more complex tasks.

<Reference article>

・What is Playing Manager?

　A playing manager is also a managerial position, so communication skills are required.

"Watanabe can't even manage his own blog properly, so can he even do his work in the field? First, let's try to master at least one of them! Kieeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeoooooooooooooooooooooooooooooo!"

　That's right. Watanabe prioritizes blogging, but due to various life circumstances, it has become difficult for him to keep up with his recent declaration of 2,000 characters per day x 5 articles. However, I am aiming for two articles a day. Quantity and quality are important.

　The story has gone off topic a bit, but if Watanabe continues to work hard, he may even get a promotion. At that point, you'll probably be confused. What should management do ? After all, I would like to say that it is a crutch to keep you from falling, and I think it would be a good idea to learn from Dr. Drager.

　This is Watanabe's strategy, but I think studying business administration will probably improve his morale. By the way, whether it's work or blogging, there are a certain number of people who want to hold back those who are working hard .

"He wasn't even bothered at all until recently. He's been on a roll lately! I'm the only one who should be on a roll! I am Ja*an!"

　It can be said that a manager's job is to deal with such people. I will say it again, one of the jobs of a manager is to prepare the workplace environment and maintain smooth interpersonal relationships in the workplace. Field work places emphasis on specialist skills, while managerial work places emphasis on communication such as interpersonal relationships. These two require fundamentally different abilities .

Watanabe meets anti-victim! ? 20% are allies, 60% are not interested and 20% are enemies! !

　Watanabe was not sharp today. Although Watanabe is usually very excited and the readers are also very excited, he seems to be the calm before the storm.

　It is possible that Watanabe was also exposed to the damage of antis for the first time.

"Be more humble, Watanabe! Well then, it's still going to be a kid's lunch. Don't you want to try steak with beer?"

　I wasn't told this directly, but I had a feeling it was something like that. However, Watanabe is not slowing down here! In fact, he plans to continue at his current pace. I declare it here.

　Watanabe's biggest purpose in blogging is to create a place for himself . Of course, the aim is to earn some pocket money, but there's no point in doing it if it's not fun. I hope I can only hang out with people who sympathize with Watanabe, who is such a natural person, and I'm sure there will be more and more haters in the future.

　As the subtitle of this blog says, `` Do not pursue those who leave, nor reject those who come .'' I'm not a real-life manager, so I can only date people I like online. I've been talking about Watanabe's grudges so far, but both his blog and Twitter are doing well. Well, it might be the best time ever.

　Real management jobs are tough. This is because you have to get along well with people you are not good at . Watanabe also wants to become an attractive person with good communication skills so that people will like him more. However, people don't act modest online. I would like to develop Watanabe's world as he pleases.

　This is a big departure from the topic of middle management, but in the sense that I also manage blogs, I should also be considered a blog manager . Through my blog, I intend to communicate with my readers and report information that will benefit them, who are my boss and company president.

　In summary, Watanabe is not suitable for real management positions. This is because I am better at increasing numbers by making creative efforts on-site. However, the more you raise the number, the closer you get to a managerial position that you are not good at, which is nothing but a dilemma.

　So, as I had previously declared, I came to the conclusion that I would study business administration and marketing. `` Watanabe, now to the president '' After all, there are many kinds of human relationships. Morale may drop in relationships. However, if you keep getting caught up in such things, you will only slow down your growth. You don't have to deal with it.

　I'm sorry that I couldn't write a silly article like I usually do this time. I never even meet the readers who came to this blog expecting such articles. Starting tomorrow, I will change my mind and make amends.

　That's why it's time for Hotaru no Hikari in this article. Some of our readers may be in management positions, but there is no need to seriously worry about interpersonal relationships. Watanabe, who is always worried, has no persuasive power to say this, but I'm sure there will be readers on his side.

　20% are allies, 60% are not interested, and 20% are enemies . Watanabe is one of the 20% of readers. And I believe that the readers are also one of Watanabe's 20% allies. I hope we can enjoy each other's lives in the coming days. See you soon.

First order congruence and Fermat's little theorem, Part 2! What are the conditions for Fermat's little theorem to hold? dragon blog

 Hello. This is Tenmei Watanabe from Dragon Blog. Last time, I explained keywords for dragon games. According to this, he explained the linear congruence formula a ≡ b (mod m), where a and b are congruent by modul m, and a – b = my. In other words, we can say that a and b have the same remainder when divided by m.

https://nabenekocom.blogspot.com/2024/02/i-will-explain-primary-congruence.html

Here, I would like to add one more explanation: my represents a multiple of m, and if m=18, it will be the number 18y. The reason why I used y here is that you can basically use any variable you like as long as there are no symbols that mean the same alphabet in the formula leading up to it. For example, to put it in an extreme way, if you set 18y to 18:00 and y=hours, there is no problem as long as it is not inconvenient for you or the person being viewed.

Now, regarding Fermat's little theorem, first let's remember how to express axaxa=a^3. A is repeated three times. Fermat's little theorem means that a^(p – 1) ≡ 1 (mod p). The expression is a little difficult, so let's actually substitute numerical values. Let p=7 be a prime number. Substituting p=7 into the formula of Fermat's little theorem, we get a^(7-1) = a^6 ≡ 1 mod 7. a^6 means multiplying a six times.

As a review before this, mod 7 calculates the remainder when divided by 7, with 7 as one period. In other words, a=0,1,2,3,4,5,6 are raised as candidates, and a=7 has a remainder of 0 when divided by 7, so 7 ≡ 0 mod 7, which overlaps with a=0, so it is excluded. Masu. Negative values ​​can also be converted to a value in the same way.

1 ^ (7 – 1) ≡ 1 ^ 6 ≡ 1 mod 7
2 ^ (7 – 1) ≡ 2 ^ 6 ≡ 64 ≡ 1 mod 7
3 ^ (7 – 1) ≡ 3 ^ 6 ≡ 729 ≡ 1 mod 7
4 ^ (7 – 1) ≡ 4 ^ 6 ≡ 4096 ≡ 1 mod 7
5 ^ (7 – 1) ≡ 5 ^ 6 ≡ 15625 ≡ 1 mod 7 6
^ (7 – 1) ≡ 6 ^ 6 ≡ 46656 ≡ 1 mod 7

One thing to note here is that a=0 is 0 no matter how many times it is multiplied by 0, so 0^(7-1)=0. Multiplying by 0 six times is still 0. In other words, if mod 7 is used, even if the number one less than that (7-1)=6 is used as an exponent, it will be 1 except for a=0.

Here, I would like to use a calculator to calculate the remainder of 109÷8. First, substitute "109", "÷", "8", and "=". "13.625" will be displayed on the calculator screen. Now subtract an integer greater than the decimal point, in this case 13. "ー" "13" "=". The screen will display "0.625", so multiply the original divided value by 8. When you press "x", "8", and "=", the desired value "5" will be displayed on the screen. This 5 is the remainder of 109÷8. When we check the calculation, we find that the calculation was correct as (109-5)÷8=13 with a remainder of 0.

Next, just to be sure, let's check whether this Fermat's little theorem is correct. The next value will be mod9.

0 ^ 8 ≡ 0 mod 9
1 ^ 8 ≡ 1 mod 9
2 ^ 8 ≡ 4 mod 9 
3 ^ 8 ≡ 0 mod 9 
4 ^ 8 ≡ 7 mod 9 
5 ^ 8 ≡ 7 mod 9
6 ^ 8 ≡ 0 mod 9
7 ^ 8 ≡ 5 mod 9
8 ^ 8 ≡ 1 mod 9

The results of mod9 were disastrous, but in mod7, 7 was a prime number. In this case, 9 is 3×3, so it is a composite number and not a prime number. Here, mod9 has two 1s, why? First, let's check whether 9 is relatively prime. Relative prime means that the greatest common divisor is 1. In the previous Dragon Game explanation, the greatest common divisor was the overlapping part of 16=2x2x2x2 and 24=3x2x2x2. In other words, 24 and 16 have 2x2x2 in common, so the greatest common divisor is 2x2x2=8.

If I write this far and explain the combination of the linear congruence and Fermat's little theorem, it will probably become quite a long article, so I would like to touch on the relationship between disjoint and 9 that I just explained and leave it for the next article. I think. I'm probably a bit inexperienced since I've just started using Dragon Games, but I'll write one article for each keyword, and one article for the summary. Since we will be mixing two keywords this time, I think the number of articles should be 2+1. Well, let's continue.

Let's check whether the values ​​up to 9 are prime with 9 in order.

The greatest common divisor of 9 and 1 is 3 x 3 and 1, so it becomes 1. First, the first greatest common divisor is 1, which is a relatively prime value. 9 and 2 are 3×3 and 2, so they are prime to each other. In other words, the second greatest common divisor is 1. Since 9 and 3 are 3×3 and 3, the greatest common divisor is 3 and they are not relatively prime. 4 and 5 are mutually prime★★. Since 6 is 2×3, the greatest common divisor is 3, so they are not coprime. 7 and 8 are mutually prime★★.

Therefore, the six elements that are relatively prime are 1, 2, 4, 5, 7, and 8. Here, the six numbers that are coprime to 9 are expressed as φ (pronunciation: phi) and are called Euler's phi function.

φ(9)=6.

mod7, which uses the prime number 7, is coprime other than 0, so there are 6 values ​​where the greatest common divisor is 1. A prime number is expressed as φ(p) = p – 1.

φ(7) = 7 -1 = 6

Returning to the topic, the composite number 9, which is the product of an integer and an integer, is a ^ φ(m) ≡1 mod m, and although a and m must be relatively prime, a ^ φ(9) = a^6 =1 mod 9. 

Taking 4 and 5, which were not 1, as an example, it becomes as follows.

4 ^ 6 ≡ 4096 ≡ 1 mod 9
5 ^ 6 ≡ 15625 ≡ 1 mod 9
6 ^ 6 ≡ 46656 ≡ 0 mod 9
7 ^ 6 ≡ 117649 ≡ 1 mod 9

Here, 6= 0 mod 9 because 6 and 9 are not relatively prime.

The number theory textbook I'm reading includes an explanation of Fermat's little theorem. If you want to know more, please read ``Number Theory for Beginners'' by Joseph H. Silverman.

Next time, I will synthesize the linear congruence and Fermat's little theorem, so please look forward to it. I spent a day researching a combination of these two keywords, but something happened. stay tuned. thank you for reading. See you soon.

How I gained 147 Twitter followers in 2 days!

good morning. This is Watanabe, the blog owner. I previously told readers that I started using Twitter. It's been a little over two weeks since I started this, but the number of followers has hyperinflated in the past two days. This is the live report.

・The volume of following at random! Become a follower by actively following

・The readers of this blog are wonderful! We work hard every day to meet the expectations of our readers.

<Reference article>

・Started Twitter

Volume of following at random! Become a follower by actively following

　Watanabe has tweeted on a different occasion than this one. At that time, I didn't have any followers at all , probably because I didn't have a huge platform . Even when I had as many followers as one hand, I would criticize politicians and my account would be suspended.

"No, Watanabe. Seriously, stop criticizing politicians because it's a death flag. It's not as if you lost your ice cream stick."

Some readers may be concerned about this.

<Related articles>

・Change the title of your blog! Get out of a rut by making regular changes

Apparently, in order to unfreeze his　Twitter account, he would need to register his mobile phone number , which Watanabe was reluctant to do. Green tea still felt sweeter. In the end, I didn't want to register my phone number, so I illegally dumped the account.

　Because of this background, to be honest, I was a little uncomfortable with Twitter. There weren't many posts, but I can't deny that I thought it was a low-return SNS where you couldn't get any followers.

　When Watanabe started blogging, he also had to deal with Twitter. Calling it advertising doesn't sound very nice, but I am convinced that blogging is an essential information medium for letting many people know about it .

　I mentioned above that it's been about two weeks since I started using Twitter, but to be honest, as the title of this article suggests, it's only in the past few days that I've figured out how to increase my followers. The reason I learned how to increase my Twitter account is because I learned that there are people who have only been using Twitter for a few months and yet have thousands of followers.

　At first, I was skeptical. "A god? A god descended to earth? I'd rather be a goddess. Amen." That's when Watanabe, who relies only on intuition, realized something. ``The way to increase followers is the same as with WordPress. It's the law of reciprocity that I learned yesterday .''

　Up until now, Watanabe had been waiting for his prey to arrive like an ant hell. However, if you don't start talking to them, the other person won't respond either . In the first place, the other person is usually not as interested in you as you think. Watanabe was what you would call overly self-conscious.

“Nabecchi is also of your age♡”

　Realizing that I was being too self-conscious, I decided to follow up on random things . However, even if you follow Twitters that are not closely related to you, it seems unlikely that you will become a follower, so I started following the Twitters that were displayed in the side menu as ``You might be interested'' one after another.

　I think a big factor was that it had something to do with my own content . This is because their appeal is completely different. Then, they will become your followers one after another. On the contrary, I received a notification every 5 minutes, and the status of ``You followed me'' or ``I got a like'' continued.

Our blog readers are wonderful! We work hard every day to meet the expectations of our readers.

　Watanabe was having palpitations as he thought to a distant memory that he hadn't been this popular since his school days. I felt like I had experienced this feeling before. That feeling is what I felt when I was investing in FX .

　Beginners in investing are not immune to investing. Therefore, I think that there are many cases where you are glued to the screen, excited and worried about unrealized gains and unrealized losses. In fact, so did Watanabe. He couldn't look away from his computer screen and couldn't help but notice Twitter notifications. "Watanabe! Calm down! Make it sticky! This must be a dream. I-Have-A-Dream!!"

　If Dr. King were alive, he might have advised us not to get involved in gambling like this. However, I couldn't stop feeling this pleasure, and ended up being glued to the screen all day yesterday.

　As a result, I had 147 followers, but the number of people I followed was around 360. Some of our readers

"What? I guess it's meaningful because you have more followers than followers . The title made me look forward to it, and you stole my heart. Tottsuaaaan."

　However, I think it is important to increase the number of followers even if you have to sacrifice your pride . There's no point in being on Twitter if you only have a few followers and no one sees you like before. It's a matter of cost performance.

　However, my future strategy is to enrich my Twitter content and increase the number of followers. This is because Twitter has restrictions such as ``A normal account cannot follow more than 400 people in a day'' and ``Unless certain conditions are met, the number of followers cannot exceed 5,000.''

　Watanabe just read the explanation and interpreted this binding on his own, so I don't know if it's correct. If any readers are interested, please check it out for yourself. The eyes know more than the ears.

　So, it's time for Hotaru no Hikari. I could go into more detail, but I have decided that it may be painful for readers to read Watanabe's lengthy text any further. Watanabe also plans to use trial and error to write articles that readers will find useful and interesting .

　Now, the total number of inflows from Twitter is less than 20 pv. At first glance, it doesn't seem like the cost performance is that good. However, compared to two weeks ago, when I didn't have any Twitter followers, it's a huge leap forward.

　As for the readers on WordPress, we don't have that many people yet, but we do have some great readers who come back every day . I take this as proof that I am interested in Watanabe's blog, so I will continue to improve it without being too self-conscious.

　If there are any developments regarding Twitter, we will report on them again, so please continue to stay with us. See you soon.

B to B is the source of overwhelming profit margin! I wondered if it could be applied to blogs as well.

 If a blogger owns a blog company that sells products such as articles, and the articles are provided to other companies, it can be said that it is a business-to-business transaction, or B to B. If the blogging company has a corporate representative, the deal will be a big one. Ultimately, it would be a good idea to aim for B2B through blog management.

Transactions between companies generate profits

　This is Watanabe, the blog owner. (ﾟдﾟ) Pokan . I didn't sleep well today, so I woke up at 2am. To be honest, I'm sleepy (lol). If possible, I would have liked to be in a dream world, chasing rabbits and fighting the queen. After all, I woke up dancing around dancing.

　Well, Watanabe is interested in the contents of my dreams while I sleep, but my friends (readers) probably aren't that interested in my dreams at all . The indifference is as much as the grains of sand scattered by lovers flying across the beach. “It’s going to be romantic♪ It’s going to be romantic (^^♪)” (I think it was the theme song for Dogon Ball...?)

　Unlike his Sarasara friends, Watanabe keeps throwing in sticky gags, but it's a wonder he doesn't get flamed. Nowadays, the only people who throw masked Molotov cocktails called gags are young people from Kaori and Japan's Watanabe. This time it became a risqué gag. introspection. Chin.

　Well, that's enough for the introduction, let's talk about transactions between companies, or B to B. In conclusion, we often hear people say, ``If you want to increase your profit margin, go for B to B transactions!'' There may be some of you out there who think that B to B will only work if the scale of your business is large. Actually, Watanabe too. I'm anxious... Marriage blue.

　However, depending on the method, B to B transactions are also possible. The specific method for doing this is described in Yu Osuka's book, ``You Decide the Price.'' Shueisha, `` Learning how to make money from the import business . '' We will name this Document 1 “Your Price”. Watanabe is by no means trying to sell you the price of this book. In fact, he shouldn't even be advertising your price.

　However, I think it's a good idea to promote good books on my blog , so I'm considering becoming an affiliate to sell good books in the future. (The good thing about Watanabe is that he is stupidly honest.) Bosori.

　Since this article is about B to B, I would like to mention some parts related to your price. In other words, they search for products that are likely to sell at major exhibitions, obtain exclusive sales rights, and sell those products to other companies . There are many benefits to selling products directly to businesses.

　"Nabecchi sells articles to companies!? With Nabecchi's sales and product capabilities, it's a shame that she'll be turned away right away. It's not time to quit! If you really want to sell, Nabecchi's partner T.R. Take it and go training in the mountains. Write 1000 articles a day. First, train your mind! A heart of steel!!!"

Differentiation to sell to companies

　If you sell your product to a company, that company will likely cooperate with you in various ways . For example, if you're pitching an article to the media, a professional editor may be able to tell you how to improve the article. Also, if you receive special advertising from an advertising company, a professional representative may be able to tell you where to improve your blog. In other words, a professional will look at your product.

　Of course, in order to get a professional to work with you, originality and novelty are required above all else. Or, if there is a rarity, there is a possibility that they will match you. Uniqueness, novelty, or rarity means that an article is different from other articles, and can be said to differentiate an article .

　Even if you write articles that are similar to other people's articles, people won't look at you; instead, you can sell because you feel the value is different from other people's. I think blogging is the business of thinking about how you can provide unique value to your friends .

　In this blog, in addition to articles on economics, etc., Watanabe plans to publish his own experiences in blog management, which worked or didn't work, from his own perspective. My recent theme is to get my fellow bloggers to know about this experience, which can't even be called know-how, and eliminate the differences that arise from knowing about it.

　If Watanabe's blog continues in the future, there is a possibility that Watanabe himself will sell to major media outlets and major advertising companies , so I think it would be interesting to publish his progress. Well, that's a long story in the distant future. If I were to open my desk drawer and find that machine there, my future would be different (lol). Take me to the future! Bubuemon!

　Now that I've read the book, let's get back to the topic of your price. Finding products that would sell at major exhibitions, obtaining exclusive sales rights, and selling these products to other companies was a trade know-how. What would happen if you applied this know-how to your blog?

How to hire a ghost rider

　Recently, Watanabe has been in the spotlight over suspicions of being a ghostwriter, but it might be interesting to ask various people to write articles for a fee . I think it's not a bad idea to ask them to write more and more if they write articles that are suitable for your blog and if you feel like you can have a long-term relationship with them.

　Of course, there are some readers who are sensitive to the idea of ​​ghostwriters. In the end, what's wrong with ghostwriting is that they try to take credit for something that someone else wrote even though they didn't write it themselves . If that's the case, simply write down the name of the person who requested the writing, and the ghostwriter problem will be resolved.

　``In Mr. Watanabe's time, the Ghost Rider was a headless rider . Times have changed, and today's Ghost Rider rides a motorcycle with a plastic bag over his head, and even drives and writes articles. He has accomplished the miraculous feat of writing all the way to the top. The evolution of humans is just astounding. ( ^ω^)..."

　In other words, if you sign an exclusive writing contract with the writing client and sell that article as a set with your own articles to major media outlets, you can earn a lot of profit with little effort. However, this business model is nothing more than a figment of Watanabe's imagination. It's similar to Ra'uta and Sata Claus in the sky. Therefore, you need to actually try it out and create a track record .

　It's almost time for Hotaru no Hikari. The story is just getting exciting, but there are too many things I want to talk about despite the excitement. If I have another chance, I would like to take that opportunity to write a continuation of this story.

　Is B to B a distant future for your friends? Although it is a distant future for Watanabe, it is not impossible that one day this blog will suddenly become popular and become B2B in no time. Blogging is like buying a lottery ticket .

　I keep drawing the lottery of articles and dreaming of winning someday. If I win the lottery, I will boast about 10 yen to all my friends. So all jokes aside, I'm also making a lot of plans. Everyone, please look ahead and try to prepare various things. Have a nice day!

References

・You decide the price, written by Yu Osuka. Learn about profitable systems from the import business” Shueisha

I will explain the primary congruence formula! Next time, I'd like to explain Fermat's little theorem and give a live commentary on the dragon game.

 Hello. This is Tenmei Watanabe from Dragon Blog. From this time on, I would like to create a dragon game that mixes multiple technical terms.

As a theme, I was planning to create a concept that combines linear congruence, Fermat's little theorem, and Fibonacci sequence, but it was more difficult than I expected, so I decided to start with the first two (linear congruence). I would like to mix up the formula and Fermat's little theorem. First, we will explain the technical terms and play the actual game.

In number theory, we place great importance on the concept of division. In other words, when one number is divided by another number, the remainder is 0. In prime factorization, 91 is divisible by 7 and 13.

It's a bit difficult, but "a is congruent to b modulo m" means a ≡ b (mod m). Here, using a real number example, if a = 92, b = 8, and m = 7, then 92 ≡ 8 (mod 7).

92 – 13 x 7 = 8 – 7 x 1 = 1 mod 7. This means that 92 and 8 each have a remainder of 1 when divided by 7. In other words, 92 and 8 are congruent (same) modulo 7. We use three lines ≡ to represent the sameness. Here, ab is divisible by m. 92-8=84 is 7×12, 92-8=84 is a multiple of 7, and when divided by 7, the remainder is 0.

Now, imagine a clock as a common example. On a 24-hour clock, the hands at 3 o'clock and 15 o'clock will point at different points. That is, 3 and 15. However, if it is a 12-hour clock, I think the hands will point to the same number 3 at 3 o'clock and 3 o'clock. 3:00 and 15:00 are 3:00 a.m. and 3:00 p.m., so if the clock is set every 12 hours, it would point to the same 3:00.

15:00 is one revolution in 12 hours, and 15:00 - 12:00 is 3:00. In the example of a and b from earlier, we can say that 15 o'clock ≡ 3 o'clock (mod 12 o'clock), and 15 o'clock is congruent with 3 o'clock modulo 12 o'clock. 15−3=12×1.

Let me give you another example. Suppose we have the formula 5a + 7b = 17. If you are an intuitive person, you will know that 5 x 2 + 7 x 1 = 17 is one answer.

Here, if we use the mod from earlier, the right side will be 17 mod 7. 17 – 7 x 2 ≡ 3 mod 7, so the remainder when you divide 17 by 7 is 3. Next, we don't know if 5a on the left side is divisible by 7, so let's call it 5a (mod 7). Next, +7b is a multiple of 7 and is an integer, so it is divisible by 7 and has a remainder of 0. So, if we compare the values ​​remaining on both sides, we get 5a (mod7) ≡ 3 (mod7).

Next, find a. It's a little complicated, but let's multiply both sides by 3. 5a x 3 (mod 7) ≡ 3×3 (mod 7). 5a x 3 ≡ 15a ≡ 14a + a ≡ a ≡ 3 x 3 (mod 7) ≡ 9 (mod 7) ≡ 7 + 2 (mod 7) ≡ 2 (mod 7). The reason why we multiplied by 3 is based on Euclid's mutual division method.

7=5×1+2 → Move 5×1 to the left and flip it over → 2=7-5
5=2×2+1 → Move 2×2 to the left and flip it over → 1=5-2×2

1=5-2x(7-5) 2=7-5 substituted into one side of 2×2
=5-2×7+2×5
 =3×5-2×7
 =1

Here, c=3, d=-2 is the answer to 5c + 7d = 1. 5 x 3 = 1 mod 7, and the right side is 1, so if you multiply both sides by 17 like the original equation 5a + 7b = 17, you get 5 x (3 x 17) + 7 x (-2 x 17) = 1 x 17. 3 x 17 (mod7) ≡ 51 ≡ 7 x 7 + 2 ≡ 2 mod 7.

On the other hand, (-2) x 17 (mod 7) ≡ -34 ≡ -6 +(-7 x 4) ≡ -6(mod7). You can leave it as -6 mod 7 here, but setting it to -6 + 7 ≡ 1 (mod 7) will make it a positive value. Therefore, a = 2 mod 7, b = 1 mod 7.

In other words, by multiplying both sides of 5a + 7b ≡ 17 (mod 7) by 3 (however, do not multiply the mod 7 by 3), 5 x 3a + 7 x 3b ≡ 17 x 3 (mod 7) is calculated as a ≡ 2 mod 7, and by substituting this a into the first 5a of 5a + 7b = 17, we can find b ≡ 1 mod 7. Here, the answer holds either 2 + 7 ≡ 9 mod 7, or 1 – 7 ≡ -6 (mod 7). Do the math yourself on this point! !

Another important point is the idea of ​​the greatest common divisor. The greatest common divisor is 16 and 24, which can be factorized as 16 = 2x2x2x2 and 24 = 2x2x2x3, so 2x2x2 = 8, which is common to both, is the greatest common divisor. In fact, 16÷8=2 has a remainder of 0, 24÷8=3 has a remainder of 0, and 8 evenly divides 16 and 24.

Here, if 5a ≡ (17 mod 7), then if the greatest common divisor of 17 and 7, which is a prime number, is 1, there is only one answer. In other words, a ≡ 2 mod 7. However, if 5a ≡ 16 (mod 24), as we found earlier, the greatest common divisor of 16 and 24 is 8, so we can find 8 answers. Let's check this out for ourselves.

This time it was long, so I only explained the technical terminology (linear congruence). Next time, I would like to investigate Fermat's little theorem and mix "linear congruence" and "Fermat's little theorem." In my opinion, I'm also good at economics, so I think it would be interesting to mix linear congruence with economics terminology.

Additionally, I would like to mix in some humor that will make you laugh while reading this blog. That's all for now. See you next time! ! Mathematics blew away! ! See you soon.

If you've just started using SNS, you may not have any followers at all, and your motivation to post content tends to be just the momentum you had when you started. Just like in real life, if you want someone to be interested in you, you need to be interested in them. So let's actively follow and like. The secret of human relationships is the law of reciprocity This is Watanabe, the blog owner. I previously mentioned on this blog that I started using Twitter. For the past few days, I haven't had time to tweet, so I haven't been able to increase the number of followers. However, instead, I am focusing on socializing with WordPress . I will write about the results of my activities at WordPress and my thoughts on them. "Nabe-kun, you've always been bad at socializing with people. But one day, after you started emulating someone who was good at socializing , your interpersonal skills improved dramatically. Socializing with people is like that! Coffee and milk... I’m a cute girl who doesn’t wear black and white. It’s so nostalgic♡” Watanabe loves cafe au lait. If he has milk in stock, he makes it himself and drinks it almost every day. He likes that it doesn't have sugar in it. As you get older, you start to worry about your blood sugar levels, so when it comes to alcohol, you drink canned Triple 0 highballs. Lemon sours seem to be popular among people in their 20s these days, and Watanabe has unexpectedly become a surfer riding the wave of alcohol. I've always been bad at interpersonal relationships . Because my personality was different from others, there were many people who treated me coldly. However, at some point, I learned that there is a trick to interpersonal relationships by imitating popular people in the group. The first trick I learned was to start talking. After all, the person who is most interested in you is yourself, and other people are not that interested in you. Therefore, if you just wait, no one will talk to you and you will end up spending a lonely time. However, there are some gods who will pick them up if you wait, and there are some who actively call out to everyone. It's hard to tell whether the positive voice that causes harm is due to lack of calculation or good intentions, but there are many people who are saved by such people. I was also one of those people who didn't like talking to people myself . However, I realized that people who talk to everyone like that are the most popular people in any group. So, I mustered up the courage to speak out on my own. I mentioned above that the people around me are not very interested in me. However, they become interested in people who actively approach them . It was during the past five years that I realized this fact. This also applies to SNS. "SNS is an online world that is different from the real world. That's why there is a unique type of communication, and SNS is when everyone chants bals over and over again." This is a big misconception. Both real life and SNS are based on relationships between people, and the skills required for relationships between users are essentially the same . Therefore, by proactively approaching others, you can eventually gain their interest. Coffee that is just waiting in a cup is a bitter experience. Some people come looking for the bitterness, but when the large entity of milk approaches them, it transforms into a cafe au lait, a sweet existence that can be enjoyed by everyone, even children . Let's like instead of saying hello So, with this introduction, I would like to move on to the theme of the title of this article. I'll tell you straight! "The best way to use SNS is to follow people as if to introduce yourself, and give them likes instead of greetings. If you can even add an edgy comment, you'll get 120 points! The moon is beautiful ♡ 8 a.m. That's it, everyone gather!!" As a side note, I am writing this article on October 3rd, so it is unlikely that I will publish it until after the 4th. We thought it would be a good idea to build up inventory in order to avoid Watanabe's continuous torrential downpours . note that. Now, Watanabe has announced that he will start selling this blog. If you search for articles within the past week, I think you will find the relevant article. I also plan to do some renovation work and expand the reference links when I have time . Since that article, I have been actively following and liking, and the number of followers on WordPress has doubled from about 20 to about 40, which is a huge sale of gratitude. The number of monthly page views as of September was also disclosed in a previous article, but in the first three days of October, we succeeded in earning a number equivalent to about half of the page views for the entire month of September. Did. Friends! thank you! ! ! Sales within WordPress is similar to sales on Twitter, and all you have to do is approach the other person and say, ``I'm interested in you.'' In Watanabe's case, his strategy was to search for keywords that seemed to be related to the articles on this blog using the purchasing blog's search engine, and follow the bloggers that appeared in the related tabs. It may not be helpful if you have a strong preference for following, but in my opinion, following is the same as introducing yourself. If you are meeting someone for the first time at work, it is common sense to introduce yourself. In other words, we follow up by saying, ``My name is Watanabe. I look forward to working with you in the future.'' Also, liking someone after following them is the same as saying hello. Likes are used to send a signal that ``I read your content. Watanabe is interested in you.'' Generally speaking, the people who follow you or respond when you like them (・∀・) are the ones who respond to everything in a fair manner. Let's take care of those people. If you get along well with such people, you can build a mutually beneficial relationship, or a win-win relationship . Let's be proactive and give the other person what they need. ``The secret of human relationships is the law of reciprocation.If you don't approach the other person, they won't turn their attention to you.Nabe-kun approaches his family's pet dog too much and is being rejected, but you should be careful with people. You know (^^♪. Love & Peace! Love & Peace!!! The letters are all jumbled (lol).” Since I'm almost over 2500 characters long, I'll call it time to get past Amagi. "No, Hotaru no Hikari! What are you talking about?" It was a mild tsukkomi, but the most important thing is to be at your own pace . This time, I tried to do a science on the reproducibility of success, but Watanabe's inspiration got in the way and I ended up creating something completely different from what I was aiming for. Watanabe works at his own pace, yes. I think everyone has different goals, whether it's blogging or anything else. However, there are certainly shortcuts to efficiently achieving each goal, and knowing the method or not makes a big difference. Watanabe is a dark hero who fights every day to eliminate these differences . Putting Watanabe's misunderstanding aside, if your colleagues are also having trouble with sales, I think it's worth giving this method a try. Emphasis! ! I aim to build a mutually beneficial relationship by providing useful information in exchange for page views, so if you are a rare friend who would like to have a part in that relationship, please join me. I hope tomorrow will be a good day too. See you soon!

 If you've just started using SNS, you may not have any followers at all, and your motivation to post content tends to be just the momentum you had when you started. Just like in real life, if you want someone to be interested in you, you need to be interested in them. So let's actively follow and like.

The secret of human relationships is the law of reciprocity

　This is 天命(Tenmei), the blog owner. I previously mentioned on this blog that I started using Twitter. For the past few days, I haven't had time to tweet, so I haven't been able to increase the number of followers. However, instead, I am focusing on socializing with WordPress . I will write about the results of my activities at WordPress and my thoughts on them.

　"Tenmei-kun, you've always been bad at socializing with people. But one day, after you started emulating someone who was good at socializing , your interpersonal skills improved dramatically. Socializing with people is like that! Coffee and milk... I’m a cute girl who doesn’t wear black and white. It’s so nostalgic♡”

　Tenmei loves cafe au lait. If he has milk in stock, he makes it himself and drinks it almost every day. He likes that it doesn't have sugar in it. As you get older, you start to worry about your blood sugar levels, so when it comes to alcohol, you drink canned Triple 0 highballs. Lemon sours seem to be popular among people in their 20s these days, and Tenmei has unexpectedly become a surfer riding the wave of alcohol.

　I've always been bad at interpersonal relationships . Because my personality was different from others, there were many people who treated me coldly. However, at some point, I learned that there is a trick to interpersonal relationships by imitating popular people in the group.

　The first trick I learned was to start talking. After all, the person who is most interested in you is yourself, and other people are not that interested in you. Therefore, if you just wait, no one will talk to you and you will end up spending a lonely time.

　However, there are some gods who will pick them up if you wait, and there are some who actively call out to everyone. It's hard to tell whether the positive voice that causes harm is due to lack of calculation or good intentions, but there are many people who are saved by such people.

　I was also one of those people who didn't like talking to people myself . However, I realized that people who talk to everyone like that are the most popular people in any group. So, I mustered up the courage to speak out on my own.

　I mentioned above that the people around me are not very interested in me. However, they become interested in people who actively approach them . It was during the past five years that I realized this fact. This also applies to SNS.

　"SNS is an online world that is different from the real world. That's why there is a unique type of communication, and SNS is when everyone chants bals over and over again." This is a big misconception. Both real life and SNS are based on relationships between people, and the skills required for relationships between users are essentially the same . Therefore, by proactively approaching others, you can eventually gain their interest.

　Coffee that is just waiting in a cup is a bitter experience. Some people come looking for the bitterness, but when the large entity of milk approaches them, it transforms into a cafe au lait, a sweet existence that can be enjoyed by everyone, even children .

Let's like instead of saying hello

　So, with this introduction, I would like to move on to the theme of the title of this article. I'll tell you straight! "The best way to use SNS is to follow people as if to introduce yourself, and give them likes instead of greetings. If you can even add an edgy comment, you'll get 120 points! The moon is beautiful ♡ 8 a.m. That's it, everyone gather!!"

　As a side note, I am writing this article on October 3rd, so it is unlikely that I will publish it until after the 4th. We thought it would be a good idea to build up inventory in order to avoid Tenmei's continuous torrential downpours . note that.

　Now, Tenmei has announced that he will start selling this blog. If you search for articles within the past week, I think you will find the relevant article. I also plan to do some renovation work and expand the reference links when I have time .

　Since that article, I have been actively following and liking, and the number of followers on WordPress has doubled from about 20 to about 40, which is a huge sale of gratitude. The number of monthly page views as of September was also disclosed in a previous article, but in the first three days of October, we succeeded in earning a number equivalent to about half of the page views for the entire month of September. Did. Friends! thank you! ! !

　Sales within WordPress is similar to sales on Twitter, and all you have to do is approach the other person and say, ``I'm interested in you.'' In Tenmei's case, his strategy was to search for keywords that seemed to be related to the articles on this blog using the purchasing blog's search engine, and follow the bloggers that appeared in the related tabs.

　It may not be helpful if you have a strong preference for following, but in my opinion, following is the same as introducing yourself. If you are meeting someone for the first time at work, it is common sense to introduce yourself. In other words, we follow up by saying, ``My name is Tenmei. I look forward to working with you in the future.''

　Also, liking someone after following them is the same as saying hello. Likes are used to send a signal that ``I read your content. Tenmei is interested in you.''

　Generally speaking, the people who follow you or respond when you like them (・∀・) are the ones who respond to everything in a fair manner. Let's take care of those people. If you get along well with such people, you can build a mutually beneficial relationship, or a win-win relationship . Let's be proactive and give the other person what they need.

``The secret of human relationships is the law of reciprocation.If you don't approach the other person, they won't turn their attention to you. Tenmei-kun approaches his family's pet dog too much and is being rejected, but you should be careful with people. You know (^^♪. Love & Peace! Love & Peace!!! The letters are all jumbled (lol).”

　Since I'm almost over 2500 characters long, I'll call it time to get past Amagi. "No, Hotaru no Hikari! What are you talking about?" It was a mild tsukkomi, but the most important thing is to be at your own pace . This time, I tried to do a science on the reproducibility of success, but Tenmei's inspiration got in the way and I ended up creating something completely different from what I was aiming for. Tenmei works at his own pace, yes.

　I think everyone has different goals, whether it's blogging or anything else. However, there are certainly shortcuts to efficiently achieving each goal, and knowing the method or not makes a big difference. Tenmei is a dark hero who fights every day to eliminate these differences .

　Putting Tenmei's misunderstanding aside, if your colleagues are also having trouble with sales, I think it's worth giving this method a try. Emphasis! ! I aim to build a mutually beneficial relationship by providing useful information in exchange for page views, so if you are a rare friend who would like to have a part in that relationship, please join me. I hope tomorrow will be a good day too. See you soon!