"...Definition 1: G = is called a labeled multistage graph, if the following conditions are met:

1. V is a set of vertices, V=VUnUVu...UV, VnV=0,0≤ij≤L,i≠j. If u€V,0≤i≤L, the level u is at is called level i, and it is also said that u is

The vertex of level i.L is called the level of G.

2.E is a set of edges, and the edges in E are all directed edges, which are represented by triples (u, v, l). If (u, v, l) €E, 1 ≤ l ≤ L, then

ueV-1vEV. Call (u, v, l) the l-th level edge of G.

3. Both and contain only a unique vertex. The only vertex in is called the source point, denoted as S, and the only vertex in is called the sink point, denoted as D..."

4.......

.......

The paper in his hand flowed through his eyes, and Xu Chuan flipped through every sentence, every mathematical formula, and even every punctuation mark in an instant.

The factorization of integers is an easy to understand and clear problem, but it is not a simple problem.

Relatively speaking, the factorization of smaller integers is a primary school arithmetic problem, but once the number is sufficiently large, such as the factorization of a 50-digit integer, it becomes a super mathematical problem.

If we use the 'trial division method' we learned in elementary school (such as 7M((4M^2)xP^2)÷(7M^2), the result is 4MP^2), even if we use an electronic computer, a person will not be able to do it in his lifetime.

.

Even assuming that human beings have been using computers to decompose this integer using trial division from generation to generation since the birth of the computer, even though centuries have passed since the invention of the computer, this 50-digit number still cannot be decomposed.

Therefore, finding a polynomial that can complete the factorization of large positive integers in a limited time is one of the ultimate dreams of mathematicians in the field of number theory.

Including Xu Chuan himself, he has always been looking forward to someone being able to complete it. Even if it is just a step forward on this road, he is extremely looking forward to it.

"...In other words, these problems are polynomially equivalent."

"In this paper, we show that all of these algorithmic procedures have polynomial time complexity relative to the length of the input data, and find a polynomial factorization algorithm that can handle large positive integer factors."

When the last sentence came into view, Xu Chuan, who had been sitting at the desk for who knows how long, finally put down the paper in his hand, breathed a sigh of relief, and rubbed his sore lumbar spine.

Although the proof of this top-level conjecture is not something that can be completely determined after just one reading, judging from the first paper and his mathematical intuition, Liu Jiaxin did it!
Chapter completed!