I just want to be a quiet scholar

Chapter 217
A Diophantine equation of the form aX^4-bY^2=1 has at most two sets of positive integer solutions.

The above sentence is an unproved conjecture by the American mathematician Walsh.

Some students in the mathematics department will complain that villains such as Goldbach, Riemann, Fermat, Catalan, and Walsh are so annoying. They are not responsible for making conjectures without proof, which makes us fail.

Yeah, they're that annoying, everyone can be that annoying, mathematics is fair, and anyone who has studied mathematics has the right to make bold guesses.

Insight makes people's perception sharp. Mathematicians who dare to make conjectures must have extremely high insight. They don't need to prove, they only need to predict.

Logical deduction is responsible for verification. Mathematicians with super logical deduction play the role of referees. They complete the proof or deny the guess.

Today in the 21st century, it is becoming more and more difficult to come up with reasonable conjectures of value, because the predecessors of mathematics have spent thousands of years almost imagining the things that should be imagined.

Most of the next work is verification, and it is also a great thing to prove a well-known unresolved conjecture.

"In the case of "Proof of the Walsh Conjecture of the Diophantine Equation", Shen Qi, you have shown a strong logical derivation ability, no problem, please submit your paper. Submit to the Journal of the American Mathematical Society or the Annals of Mathematics, Why not?" Mueller said after reading Shen Qi's paper.

"Journal of the American Mathematical Society" and "Annual of Mathematics" are all mathematics journals run by the United States. They are also known as the four major international mathematics journals along with the "Acta Mathematica Sinica" run by the Swedes and the "Inventions of Mathematics" run by the Germans.

"Okay, I'll submit the paper later." Shen Qi originally planned to submit this paper to the "American Transactions on Mathematics" or "Pacific Journal of Mathematics", which is a top-notch mathematics journal in the United States and a second-class international mathematics journal. Since Professor Muller encouraged He submitted manuscripts to the four major international journals, so let's do it.

"The co-first author is Oh...Yeah?" Professor Muller tentatively pronounced.

"Yes, Ou~~ye, my girlfriend." Shen Qi corrected Mu Le's pronunciation.

"She is Chinese?"

"Chinese."

"Strange pronunciation, interesting name." Mueller finished reviewing Shen Qi's thesis, and handed the paper to Mary: "Mary, you specialize in number theory, take a look."

After receiving Shen Qi's paper, Mary's expression was wonderful, she believed it was true but kept doubting it, she gritted her teeth and tried her best to restrain herself, she wanted to overthrow it but the goal was impeccable, so she could only bite her teeth and swallow it in her stomach.

No one is more familiar with Shen Qi's paper than Mary.

As far as this paper on the proof of the Walsh conjecture of the Diophantine equation is concerned, Mary may know the author Shen Qi better than Ouye.

The person who knows you best is often not your wife, but your sworn enemy.

In this paper, Shen Qi used Thue-Siegel's Padé approximation method for binomial functions to accurately solve Thue's equation and Thue's inequality.

The effective algebraic approximation of this hypergeometric method is extremely skillful in Shen Qi's hands, and it is more pure than when he was at the beginning of the year.

Shen Qi's approximation method is too familiar to Mary, and she quoted the conclusions of Shen Qi's method in her doctoral dissertation.

He became stronger again... Mary's breathing became short of breath, her chest heaved violently, and the lack of sleep recently caused her shortness of breath and chest tightness.

However, what is strange is that after the end of PAD, Shen Qi did not quote Mary's unique skill - dealing with non-zero algebraic integers, which made Mary feel sad, sad, and even a little bit lost.

At the beginning of this year, he obviously used my unique skills... Mary glanced at Shen Qi bitterly, not reconciled.

The situation is becoming clear. Since Shen Qi does not use non-zero algebraic integers after Thue-Siegel's Padé approximation of the binomial function, then he must give up the Evita proof—Marie's other hand Unique job.

Uneasy, Mary flipped through Shen Qi's thesis to the last few pages. Sure enough, this Chinese kid!
Shen Qi boldly used the Gap criterion combined with the reduction method, and cleverly transitioned to the quartic equation ζ=aω^v+b/ a1ω^v+b1, which is equivalent to determining all the square numbers in the sequence.

It was almost a fatal blow, leaving Mary devastated, so powerless, she felt hollowed out of her body.

In the end, Shen Qi perfectly proved that the Diophantine equation of the form aX^4-bY^2=1 has at most two sets of positive integer solutions.

Walsh's conjecture was thoroughly proved by a 21-year-old Chinese young man with a brand-new and concise method.

Mary's face fluctuates from white to red. She is seven years older than Shen Qi. She graduated from the Department of Mathematics of a prestigious German university with a Ph.D.

She used to be very proud, but now she is ashamed.

Compared with Shen Qi's proof method, Mary's doctoral thesis is slightly inferior.

Mary has to admit even if she doesn't want to admit it, Shen Qi is more like a real doctor of mathematics.

The young man from China conquered the female doctor from Germany with his proficient and fluent mathematical skills and his four-two-handed operation.

If you are not convinced, you have to obey. The facts are in front of you. People who study mathematics can be defeated, but they must not ignore the truth.

Breathing became more and more rapid, and Mary felt hot all over. She took off her small suit jacket, and only heard a crisp sound of "pia" and a button snapped off in the process of taking off the jacket.

The original habitat of the small black button was Mary's close-fitting white shirt. The rapid breathing caused the rise and fall of Mary's chest to increase, and the shaking frequency increased.

The chest of the female doctor from Germany trembled just like that, and she unintentionally forcibly burst open her close-fitting white shirt, and the buttons were blown off.

This……

The three men were astonished. Mary's unique skill was so awesome, her chest trembled, the buttons snapped, the strength was amazing, and the elasticity exploded.

"Excuse me, I'm going to change clothes." Mary pretended to be calm, got up and left the office as if nothing had happened.

"This woman doesn't wear a bra." Jonas spread his hands and said.

"German women are like that," Müller explained.

"Fantastic." Shen Qi was convinced, the German woman would hurt someone with a hidden weapon if she disagreed with her, it was very dangerous.

Mary returned to the office after changing her clothes, and the regular academic meeting of Professor Muller's research team continued.

After friendly negotiation and full discussion, the meeting agreed that Shen Qi's paper "Proof of the Walsh Conjecture of the Diophantine Equation" was submitted to the "Journal of the American Mathematical Society".

And there was a long debate on the second topic, the Riemann zeta function ζ(2n+1).

The two sides in the debate were Shen Qi and Mary. Muller gave a pertinent comment on the two different views. He said: "My original intention was to let Mary and Shen Qi cooperate in depth, but now it seems that the same topic Two different solutions have emerged. I declare today's meeting closed, and after half a month I hope to see the latest progress in seeking common ground while reserving differences."

(End of this chapter)