Before returning to the college entrance examination, I became popular in the science circle

Wu Tong has always been true to his word. When he said he was returning to the world of mathematics, he took immediate action.Goldbach guessed that this topic had been delayed for too long, and the piecemeal study was too fragmentary. After all, it was better to devote oneself to it.

She began to regularly go to the mathematical research center, the library, and the dormitory, and devoted herself wholeheartedly to the research on Goldbach's conjecture. The manuscripts of her predecessors were repeatedly studied by her, including the sieving method, the circle method, and various other methods. Wu Tong has tried all the methods used to overcome Goldbach's conjecture. She needs a tool to overcome Goldbach's conjecture.

It is said that the sifting method has come to an end. After using it personally, Wu Tong did not agree with this view, and she finally confirmed it.It is still necessary to improve the screening method and lay the foundation for a solid ladder to climb to the top of Gecai.

Wu Tong wants to complete the research on the information involved in Ge Guai as soon as possible. If everything goes well, he will complete this topic in March. After that, he may have time to go home for a while. Then he will wait for one to two months for his graduation defense and prepare for graduation. Can.

The thought of being able to go home and stay for one to two months made Wu Tong even more motivated.Every question has an answer.Studying hard, Wu Tong is happy and immersed. The difficulties that hinder the world from moving forward are just a more difficult step for her, not insurmountable.

Wu Tong finally chose the circular method to introduce the sieve method, and made supplementary innovations to the sieve method.

Generating functions are often used when studying many number theory problems.For example, when studying the distribution of prime numbers, we will use Dirichlet series... By applying Perron's formula, the analytical properties of F(s) can be used to study many product number theory problems...

Through more clever use of the circle method, previous generations have proven that almost all even numbers satisfy the Strong Goldbach conjecture...

The sifting method is actually a broader idea.Using this method, some number theoretical quantities can be estimated.To take the simplest example, if π(x, z) is used to represent the number of positive integers whose size does not exceed x but all prime factors are greater than z:

π(x,z) is a typical sieve function.The sieve method is a method used to estimate such functions.The sieve method plays an important role in the Goldbach problem. To be precise, this form of sieve method is used in the study of {a, b} problems...

Wu Tong thought about the sieve method and the circle method, and how to combine them bit by bit to create a ladder to conquer Gecai.

N=p1+p2+p3(素数p1，p2，p3均≥3)的解数···

The problem of A+B is ultimately a complex expression of Goldbach's idea. Every large even number N can be expressed as a+b. The number of prime factors of AB does not exceed A and B respectively. When A=B=1, the problem naturally returns to the original expression. Any even number greater than 2 can be written as the sum of two prime numbers.

In the form of 1+1, the road ahead is still Goldbach's conjecture itself, and the number of prime factors is 1.

When searching for the best way to combine the sieve method and the circle method, Wu Tong thought again that around this time at the beginning of last year, she was reminded by Lu Xiao in the library that the topological sieve method was originally introduced to people by Professor Zelberg. After some attempts to extend Goldbach's conjecture and launch a charge, she remembered her own infinite group proof method...

Thoughts collided here, and sparks splashed into a new chapter. Wu Tong looked out the window. At this time, the spring breeze was blowing, the earth was warming up, and the greenery was dyed. Spring, summer, autumn and winter, the four seasons are a cycle. The charge of Goldbach's conjecture, Is it not a reincarnation?
The ultimate state of the sieve method...the closed orbit integral and the residue theorem of the circle method, the infinite topology of group theory...all were intertwined in Wu Tong's mind, forming a beautiful chapter.Wu Tong's eyes were focused on the budding winter jasmine outside the window. She thought that she had found a way to climb Mount Everest. She just needed to complete the construction of the road. Climbing to the top would be a natural thing.

Wu Tong has done a lot of building bridges and paving roads before, and now he can be said to be very familiar with it.The writing is silky smooth, and the steps of climbing are condensed on the tip of Wu Tong's pen.

Although she has not done anything new in mathematics research in the past six months, all her research is based on mathematics. With sufficient training, Wu Tong has made great progress in the mastery and accumulation of mathematics.

Nowadays, when we really engage in mathematical research, it is natural that the wind helps the fire.A prairie fire started in an instant.The progress was smooth, exceeding Wu Tong's expectations. It was a result of trickles and accumulations.

Wu Tong was not as inspired as before, working hard all night long.She seems to be in a special state every day now, still maintaining the three-point-one-line step by step, but Cai Yi, who follows Wu Tong every day, can see that Wu Tong is not in the right state at this time, and she is even more It's like being immersed in your own world.

Cai Yi and the others had enough knowledge of Wu Tong's special state, although Wu Tong's state this time was different from usual.However, they still responded quickly and arranged for An Wenshu to serve as a living assistant and follow Wu Tong to help her avoid any disturbances she might encounter on the road.At the research center, Professor Zhou was contacted to avoid the disturbance to Wu Tong from the top and bottom of the Numerical Research Center.

Wu Tong has been immersed in this special state, resting, eating, doing research, repeating the cycle for a week.Thick manuscripts of deductions piled up on Wu Tong's desk. Unfortunately, she put pen to paper and wrote down the last stroke of the proof method she named the sieve circle method. The dawn of the crown jewel of number theory, the mountain of Gechai, was conquered. Light up.

"Professor Zhou, starting from tomorrow I will go into retreat and concentrate on conquering Goldbach's conjecture. I will not come to the Numerical Research Center for the time being!" Later, Wu Tong knocked on the door of Professor Zhou's office opposite the test and entered the office to report to him. road.

Zhou Wenping was reviewing students' papers, but his horizons were raised by Wu Tong's achievements. Every time he saw students' papers, he had to keep himself calm. There is only one Wu Tong, and not everyone is a super person like Wu Tong. student.

Just as he was thinking that Wu Tong was currently in a special research state, and he might not know when he would give them another big result that would shock the world, he saw Wu Tong pushing in the door.He couldn't help but have shock on his face, "Wu Tong, you have..."

Did you figure out my brother's guess?He didn't dare to ask this question. Wu Tong had only been back for less than ten days. If he had already conquered Gecai in one fell swoop, he felt that he needed a quick-acting heart-saving pill!
"It's not that fast, Professor Zhou!" Wu Tong's words made Zhou Wenping's heart drop a little, and he said, guess it's so easy to get it done, it won't take hundreds of years, and it won't take a few hundred years. People make great achievements.

But then Wu Tong said again: "I have found a way out and made a method to conquer Gecai. All that is left is to go into retreat and substitute Gecai into the proof. Professor Zhou will wait a week or two for my surprise!" "

"Ah..." It's really a big surprise. Can you figure it out in a week or two?