Chapter 456 (1/2)

Chapter 459

in a word, Gu shanzhicun conjecture means that the elliptic curves above the rational number field can be modeled.

The problem seems so simple that ordinary undergraduates can understand it.

But this conjecture has puzzled mathematicians all over the world for more than 50 years.

Even in the period when Gushan Zhicun conjecture was just put forward, the proof process can be described as difficult.

It was not until 1993 that wiles announced the proof of Fermat's theorem that the proof of Gushan's conjecture took a big step forward.

However, in recent years, as the number of mathematicians who devote their energy to the conjecture of Gushan village is becoming less and less, the road to explore the conjecture has become dark again.

In fact, every proof of a mathematical guess is like a long run.

Generation after generation, a mathematician, struggling to run, will continue to pass the baton in their hands.

Do not know the end point, do not know the direction, the people of the same trade constantly fall down, new running constantly join.

Now, the baton that Gushan village conjectures has been passed to Cheng Nuo's hand.

Around, there are not a few of them.

In front of us, we can't see any light.

Cheng Nuo can only follow the path of the predecessors, groping forward, looking for the light breaking the darkness, trying to rush to the end of the game.

…………

For the convenience of communication, Cheng and the other two professors in his group directly put their offices in an office in the clay Institute of mathematics.

The general direction of the proof work is controlled by Cheng Nuo.

Two mathematics professors from Denmark and Belgium filled in the details.

For the proof of Gushan Zhicun's conjecture, Cheng Nuo, like most of his predecessors, regards Fermat's theorem as his breakthrough.

In the language of mathematics, Fermat's theorem is a necessary and insufficient condition for Gushan Zhicun's conjecture.

In other words, after a certain deduction, the theorem of Gushan Zhicun can prove Fermat's theorem.

However, the existence of Fermat's theorem can not prove the correctness of Gushan Zhicun's conjecture.

In a certain sense, Fermat's theorem can only show that Gushan Zhicun's conjecture is true on the semi stable elliptic curve.

However, Fermat's theorem is still of great significance for the proof of Gushan Zhicun's conjecture.

Cheng Nuo also decided to start from this direction and try to prove the method.

A person in the office, has maintained a movement for more than an hour Cheng Nuo finally felt that he had caught the glimmer of inspiration, took the pen, and Shua Shua wrote down the inspiration on the draft paper.

According to Fermat theorem n = 4, the research object is defined as elliptic curve e: y ^ 2 = x ^ 3-x. let β be a prime number, and the number of solutions of this equation in finite field ft is β = 1, 3, 5 They are... ”

“…… Next, we use the module group Γ (1): = SL2 (Ζ) to act on the complex upper half plane H = {Z ∈ C | im (z) > 0} by fractional linear transformation. ”

“…… In the third step, suppose that E: y 2 = ax 3 + by 2 + CX + D is an elliptic curve over the rational number field Q, then we need to consider its ”reduction” in the coefficient module prime number. In addition, isomorphic elliptic curves may give completely different ”reductions”: consider y 2 = 27 x 3 - 3 x and y 2 = x 3 - x, the former is not an elliptic curve on F3, the latter is an elliptic curve on F3. Therefore, it is concluded that ①: isomorphic elliptic curves should be regarded as equivalent! ”

…………

Like Cheng Nuo and his team, the other seven certification teams started their research work under the leadership of their team leaders as soon as they got the task.

After all, they are not only racing against the three-year research cycle, but also competing with other groups.

The distribution of researchers is proportional to the difficulty of conjecture. The starting line was almost the same.