Convinced

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

The above statement is an unproven conjecture by the American mathematician Wash.

Some Mathematics Department students complain that bad guys like Goldbach, Riemann, Fermat, Catalan, and Wash are so annoying; they irresponsibly make conjectures without proof, causing us to fail our courses.

Yes, they are just that annoying. Everyone can be that annoying. Mathematics is fair; anyone who has studied mathematics has the right to boldly make conjectures.

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

Logical reasoning is responsible for verification, and mathematicians with exceptional logical reasoning skills act as judges, either proving or disproving conjectures.

In the 21st century, it is becoming increasingly difficult to propose valuable and reasonable conjectures, because our mathematical predecessors have spent thousands of years imagining almost everything that could be imagined.

The rest of the work will mostly be verification; proving a famous but unresolved conjecture is also a remarkable task.

"In the case of the Proof of Diophantine Equation Wash Conjecture, Shen Qi, you demonstrated extremely strong logical reasoning ability. No problem, submit it. Submit it to the Journal of the American Mathematical Society or the Annals of Mathematics, why not?" Muller said after reading Shen Qi's paper.

The Journal of the American Mathematical Society and the Annals of Mathematics are both American-run mathematics journals. They, along with the Swedish-run Journal of Mathematics Sinica and the German-run Inventiones Mathematicae, are known as the four major international mathematics journals.

"Okay, I'll submit it in a bit." Shen Qi originally planned to submit this paper to National First Prize Bulletin of the American Mathematical Society or the Pacific Journal of Mathematics of Mathematics, which are second-tier internationally. Since Professor Muller encouraged him to submit to the Top Four Journals, he decided to do so.

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

"Yes, oh~~ye, my girlfriend." Shen Qi corrected Muller's pronunciation.

"She's Chinese?"

"Chinese."

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

Mary's expression was priceless as she took Shen Qi's thesis. She believed it wholeheartedly yet remained skeptical, gritting her teeth while trying her best to restrain herself. She wanted to refute it, but her target was impeccable, so she could only grit her teeth and swallow her anger.

No one knew Shen Qi's paper better Mary.

Regarding this paper proving the Wash Conjecture of the Diophantine equation alone, Mary probably knows the paper's author Shen Qi, better than Ou Ye.

The person who understands you best is often not your wife, but your mortal enemy.

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

Shen Qi has mastered the use of this hypergeometric method for effective algebraic approximation with unparalleled skill, achieving a level of sophistication even surpassing his proficiency at the beginning of the year.

Mary was very familiar with Shen Qi's approach of getting closer; she had cited the conclusions drawn from this Shen Qi in her doctoral dissertation.

He's gotten stronger again... Mary's breathing became rapid, her chest heaving violently; recent sleep deprivation had caused her shortness of breath and chest tightness.

However, what was unexpected was that after Padé approximation ended, Shen Qi did not use Mary's specialty—the handling of non-zero algebraic integers—which made Mary feel sad, heartbroken, and even somewhat disappointed.

At the beginning of this year, he clearly used my special skill... Mary glared at Shen Qi resentfully, unwilling to accept it.

The situation is becoming clearer. Since Shen Qi does not use non-zero algebraic integers after Tuer-Siegel's Padé approximation of binomial functions, he will inevitably abandon Evitzer proof —another of Mary's tricks.

With trepidation, Mary flipped through Shen Qi's paper to the last few pages, and sure enough, it was that Chinese kid!

Shen Qi boldly used the Gap criterion combined with reduction methods to cleverly transition to the quartic equation ζ=aω^v+b/a1ω^v+b1 being equivalent to determining all squares in the sequence.

This was almost a fatal blow, leaving Mary disoriented, utterly powerless, and feeling completely drained.

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

The Wash Conjecture was thoroughly proven by a 21-year-old Chinese man using a completely new and concise method.

Mary's face flushed and paled in turns. She was seven years older than Shen Qi and had graduated from the Mathematics Department of a prestigious German university with a doctoral degree.

She had once been very proud, but now she felt utterly ashamed.

Compared to Shen Qi's proof method, Mary's doctoral dissertation is somewhat inferior.

Whether Mary wanted to admit it or not, she had to admit that Shen Qi was more like a true mathematics PhD.

A young Chinese man, with his skillful and fluent mathematical techniques and effortless maneuvering, won over a German female PhD student.

Whether you like it or not, you have to accept it. The facts are right in front of you. Mathematicians can be defeated, but they can never ignore the truth.

Mary's breathing became increasingly rapid, and she felt hot all over. She took off her blazer, and as she did so, she heard a crisp "pia" sound as a button popped off.

The small black button had originally been placed on Mary's close-fitting white shirt; her rapid breathing caused Mary chest to rise and fall more dramatically, and the frequency of her trembling increased.

The German female PhD student's chest trembled slightly, and she unintentionally forced open her close-fitting white shirt, causing the buttons to pop off.

This...

The three men were astonished. Mary's skill was incredible; with a slight jerk of her chest, a button popped open with amazing force and explosive elasticity.

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

"This woman isn't wearing a bra," Jonas said, shrugging.

"German women are all like that," Muller explained.

"Impressive." Shen Qi was impressed. German women would use hidden weapons to injure people without warning; how dangerous.

After Mary changed her clothes and returned to her office, Professor Muller's research team's academic meeting continued.

After friendly consultation and full discussion, the meeting agreed to submit Shen Qi's paper, "Proof of Diophantine Equation Wash Conjecture," to the Journal of the Journal of the American Mathematical Society.

They then engaged in a lengthy debate on the second topic: the Riemann zeta function ζ(2n+1).

The debate was between Shen Qi and Mary. Muller offered insightful comments on the two differing viewpoints, stating, "My initial intention was for Mary and Shen Qi to collaborate more deeply, but it now appears that two different solutions have emerged for the same topic. I hereby adjourn today's meeting, and I hope to see the latest developments in seeking common ground while reserving differences in two weeks."