He boasted that he had solved prime factorization, but in reality it seems he was still a little early resurrection spell by Nada 20231001

Hello. This is Nada. This time, there was an error in the previous article about solving prime factorization, so I would like to post a rewritten article.

First, let's talk about prime factorization of 3511×1429=5017219.

5017219=79mod108, 5017219=58mod109, 5017219=103mod116,

79mod108-58mod109=a

(5017219-108×1429)-(5017219-109×1429) = 4862887-4861458 = 1429

58mod109-103mod116=7a

(5017219-109×1429)-(5017219-116×1429) = 4861458-4851455=1429×7

Substitute the right-hand side a of the first equation into the right-hand side 7a of the second equation.

58mod109-103mod116=7x(79mod108-58mod109)

4862887×7-4861458×7

(8×58)mod109=103mod116+(7×79)mod108

38891664

28mod109 = 103mod116+13mod108

38891664 = 4851455 + 4862887×7

28mod109 = 88mod224

38891664 = 38891664

From now on, think for yourself!

28+109p = 88+224q is also fine.

Modifications such as 79mod108=5017219-108a=79+108s+108a are also possible. Extreme story. You can also replace it with 79mod108=5017219. I'll think about it some more, so if you have any interesting suggestions, please drop them in the comments. See you soon.

(Supplementary information) What does 28 mod 109 = 88 mod 224 mean? 28 mod 109 is (58mod109)x8. On the other hand, 88mod224 has also been x8ed, but when you return it to the value before x8ing, (88mod224)/8=11mod28, and although I don't know if it's a coincidence, you can see that it is the same as 3511=11mod28. The challenge this time is to factorize 3511×1429 into prime factors, so please check other samples to see if this is correct.