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

The above sentence is a conjecture that the American mathematician Walsh did not prove.

Some math students complain that bad guys like Goldbach, Riemann, Fermat, Catalan, and Walsh are so annoying that they are not responsible for making unproven conjectures, which hurts us.

Yes, they just hate it, everyone can hate it so much, math is fair, and anyone who has studied math has the right to make a bold guess.

Insight sharpens people's perceptions, and mathematicians who dare to come up with conjectures must have extremely high insight, they don't need to prove, they just need to predict.

Logical derivation is responsible for verification, and mathematicians with strong logical derivation play the role of referees, who complete proofs or disprove guesses.

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

Much of the rest of the work is to verify, and it is also a remarkable thing to prove a famous conjecture that has been left unsolved.

"In the case of "Proof of the Walsh Conjecture of the Diophantine Equation", Shen Qi, you have demonstrated a strong ability to derive logic, no problem, submit it. Why not submit it to the Journal of the American Mathematical Society or the Annals of Mathematics?" said Muller after reading Shen Qi's paper.

The Journal of the American Mathematical Society and the Annals of Mathematics are both American-run mathematics journals, and they are known as the four major international mathematics journals, along with the Swede-run Acta Mathematica Sinica and the German-run Mathematical Inventions.

"Okay, I'll post later. Shen Qi originally planned to submit the paper to the American Mathematical Transactions or the Pacific Journal of Mathematics, which are first-class mathematics journals in the United States and second-class in the world, but since Professor Mueller encouraged him to submit his paper to the four major international journals, he should do so.

The co-first author is Oh...... "Professor Mueller tried his pronunciation.

"Yes, Ou~~ Ye, my girlfriend. Shen Qi corrected Mueller's pronunciation.

"She's Chinese?"

"Chinese. ”

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

After receiving Shen Qi's paper, Mary's expression was wonderful, believing it to be true but remaining skeptical, gritting her teeth and trying her best to restrain herself, wanting to overthrow it, but the goal was flawless, so she could only grit her teeth and swallow it in her stomach.

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

In the case of this paper proving the Walsh conjecture of the Diophantine equation, Mary may know the author of the paper 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 uses the Tour-Siegel's Pard approximation method for binomial functions to accurately solve the Diagram's equation and the Diagram's inequality.

The effective algebraic approximation of this hypergeometric method was used by Shen Qi with great skill, and it was more refined than when he was at the beginning of the year.

Shen Qi's approach was all too familiar to Mary, and she cited Shen Qi's approach in her doctoral dissertation.

He's getting stronger again...... Mary's breathing became rapid, her chest heaved violently, and her recent lack of sleep had caused her to be short of breath and tight.

However, unfamiliarly, after the end of Pader's approach, Shen Qi did not quote Mary's unique trick - non-zero algebraic integer processing, which made Mary feel sad, sad, and even a little lost.

At the beginning of this year, he obviously used my unique skills...... Mary glanced at Shen Qi hatefully, unwilling.

It became clear that since Shen Qi did not use non-zero algebraic integer processing after Tue-Siegel's Pard approximation of binomial functions, he would inevitably abandon the Evitzer method --- Mary's other skill.

Nervous, Mary flipped through Shen Qi's paper to the last few pages, and sure enough, this Chinese boy!

Shen Qi boldly used the Gap criterion combined with the reduction method to skillfully transition to the quadratic equation ζ=aω^v+b/ a1ω^v+b1 is equivalent to all the squares in the determined sequence.

It was almost a fatal blow, leaving Mary devastated and powerless, feeling hollowed out.

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

Walsh's conjecture was thoroughly proved by a young Chinese man under the age of twenty-one in a new, concise way.

Mary's face turned white and red, she was seven years older than Shen Qi, and she graduated from the mathematics department of a prestigious German university with a doctorate.

She used to be very proud, but now she has no place to be ashamed.

Compared with Shen Qi's proof method, Mary's doctoral dissertation is omitted.

Mary didn't want to admit it, but she had to admit that Shen Qi was more like a real doctor of mathematics.

A young man from China used his skillful and fluent mathematical skills to conquer the German female doctor.

If you don't accept it, you have to accept it, the facts are in front of you, and those who study mathematics can be defeated, but they must not ignore the truth.

Breathing more and more rapidly, Mary was feverish, she took off her blazer, and in the process of taking off her coat, she heard a crisp sound of "pia" and a button popped off.

The original habitat of the small black buttons was Mary's close-fitting white shirt, and the rapid breathing made Mary's chest rise and fall wider, and the frequency of shaking increased.

The German female doctor's chest shook like this, and she inadvertently forcibly broke open the close-fitting white shirt, and the buttons were broken.

This......

The three men were surprised, Mary's hand was too awesome, her chest shook, the buttons collapsed, the strength was amazing, and the elasticity exploded.

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

"This woman doesn't even wear a bra. Jonas said.

"German women are like that. Mueller explained.

"Awesome. Shen Qi was convinced, and the German woman secretly hurt people if she didn't agree with her, so dangerous.

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

After full discussion through friendly consultation, the conference agreed to Shen Qi's paper "Proof of Walsh's Conjecture of Diophantine Equations" and submitted it to the Journal of the American Mathematical Society.

The second topic, the Riemann Zeta function ζ (2n+1), was debated for a long time.

The two sides of the debate were Shen Qi and Mary, and Mueller gave a pertinent comment on the two different points of view, saying: "My original intention was to have Mary and Shen Qi work together in depth, but now it seems that there are two different solutions to the same problem. I declare that today's meeting is closed, and in half a month I hope to see an update on the progress of seeking common ground while reserving differences. ”