In the published paper, Shen Qi used PLAN-A to complete the proof of Walsh's conjecture.

Suppose (X,Y) is a solution of Eq. (t+1)X^4-tY^2=1, satisfying Y>1, (x,y) is the corresponding adjoining solution, and N=√x^2+y^2t, then for a positive integer t0 satisfying t0∣t and t0^2≤t, there is P(x,y)=t0^2.

This is the core step of proving Walsh's conjecture, defining r0 as a positive integer satisfying (e^2.37ε2/8)^1-r0≤∣fq∣≤(e^2.37ε2/8)^-r0, and Shen Qi used PLAN-A in his paper.

In PLAN-A, Shen Qi makes r0=1, ±B1q≠A1p and 2∣fq∣(e^2.37ε2/8)Y1>1 satisfies ∣±√-1(xi-yi√-t)/(xi+yi√-t)-X^1/4∣<1/8.

So, Mr. Walsh's guess 37 years ago was correct.

This suspicion was confirmed by a 21-year-old Chinese student.

As a result, Shen Qi has received a number of honors and awards, and has made a name for himself in the Chinese and American mathematical circles.

And the bunch of mathematical symbols that Wu Lao has just written down represent PLAN-B, that is, another way to prove the core proof step of Walsh's conjecture.

It turned out that Mr. Wu had read my paper published in the Journal of the American Mathematical Society. Shen Qi knew it in his heart.

In fact, Shen Qi only realized PLAN-B not long ago, thanks to the pressing of the Princeton math gangster group.

But at that time, Shen Qi had already published a paper based on PLAN-A.

PLAN-B is a supplement to him rather than a rigid need, so Shen Qi did not immediately refine the specific operation plan of PLAN-B, and left a thought in his heart.

Then, Shen Qi was told that he had won the Chern's Prize in Mathematics, and that he could not change the published PLAN-A during this special period.

A few days ago, Shen Qi upgraded the math level to level 10, and he completely comprehended PLAN-B in the virtual scene in his mind.

Therefore, Wu always wanted to talk to me about PLAN-B, but he didn't want to explain it too clearly, everything was in plain sight...... Shen Qi walked to the whiteboard, picked up the water-based pen and wrote:

N2≥N1^7/6t^2

After writing, Shen Qi humbly asked for advice: "Please ask Elder Wu for advice." ”

"You're young, but pragmatic, and I like pragmatic young people. Wu Lao smiled, wiped Shen Qi's ≥ with his hand, and gave N2 a cube.

So Shen Qi's answer N2≥N1^7/6t^2 was changed to "N2^3 blank N1^7/6t^2".

"Wu Lao is really skilled. Shen Qi bowed his hand in convincing, and then said: "But Xiaosheng still has a way to live." ”

Shen Qi filled in the blank space with ≤, added an N1 before N2^3, and then erased N1^7/6t^2 and replaced it with 54B^2t^1.5

So the latest answer became:

N1 N2^3≤54B^2t^1.5

"Young people have a lively brain, a wide range of ideas, and a terrifying future. Wu Lao said with a smile, and then wrote down a very complicated formula:

2t2^2/√t+1N1^4（N2/N1）^4=...... 8/（e^0.99ε1）^2（3N2/N1）

"Hahaha!" Shen Qi looked up to the sky and laughed, and gave a thumbs up: "Obeyed, Xiaosheng served, Wu Lao really Taishan Beidou, and the canopy disappeared in the middle of talking and laughing." ”

"Is there a countermeasure?" Wu Lao asked, expecting Shen Qi's answer.

"There is still a plan, to break the kettle. Shen Qi couldn't help but praise the academician for being an academician, and his level was indeed high.

Then Shen Qi wrote down a more complex line:

∣（4B√-t+4A）（u+v√-t）^4-（4B√-t-4A）（u-v√-t）^4∣......=8N1^8t2^2，t2＜√t

The others in the room looked pensive or dazed.

"Hahaha!" Academician Wu laughed heartily and said, "Different paths lead to the same end." ”

"Hahaha!" Shen Qi smiled very happily, and the only person who understood him was Academician Wu: "Different paths lead to the same end." ”

Two mathematicians, an old man and a young man, appreciate each other, and seem to have become old friends.

The room full of people look at me, I look at you, I don't dare to speak, I don't know what to say, I just think this should be a high-end argument, very valuable for research.

"Wipe it, it's actually useless. Wu Lao suddenly shook his head and said to Shen Qi.

"It's really useless, fennel beans, it's enough to write one. Shen Qi wiped all the handwriting on the whiteboard, and his ideological realm was further improved.

"This ......" The others were speechless, what the hell are you two doing? Write and erase, wipe and write, write and wipe all the way clean, guess the riddle?

"Professor Sun, may I ask what happened between Shen Qi and Academician Wu?" Zhou Yu'an asked in a whisper with a strong desire for knowledge.

"Heaven must not be divulged. Sun Erxiong said mysteriously.

"So, at the end of my report today, thank you for your participation, and now, I would like to invite Academician Wu to give us a few words. Shen Qi felt that it was almost over, and according to the usual practice, he wanted to ask the leader to make a concluding speech.

"Three sentences, don't play with fiction in the study of mathematics, live in loneliness calmly and patiently, learn endlessly, be cautious in words and deeds, and dismiss the meeting. After Wu Lao finished speaking, he left with his hands, walked to the door and turned around and said, "Shen Qi, you come out with me." ”

Shen Qi nodded and left with his hands in his hands.

Leaving a room full of people talking.

"Shen Qi is going to get Academician Wu's individual guidance. Zhou Yu'an didn't understand too much what Shen Qi was pretending to be, what he could understand was that Shen Qi should have pretended to be a coercion and shocked everyone.

"Shen Qi is young and promising. ”

"This young man is good, material, unassuming, and free to put away. ”

"Such a calm and measured young man is rare in these years. ”

"People who can go to Princeton's math department for further study are really talented. ”

Everyone praised Shen Qi, and a new star in the Chinese mathematical community was rising.

In a corner of the University of Hong Kong, Academician Wu and Shen Qi communicated alone.

"I read your paper published in the Journal of the American Mathematical Society, where assuming a and b are positive integers, then Walsh's Diophantine equation has at most two sets of positive integer solutions. Shen Qi, your proof method is the most perfect, I just had a whim, the old man is talking about juvenile madness. Academician Wu said.

"Thank you for your advice. ”

"It's not a point, I'm just looking for you to verify my idea. ”

All in all, Academician Wu found some inspiration from Shen Qi's PLAN-A, so he tinkered with PLAN-B and played a game with Shen Qi.

Academician Wu's old husband talked about the PLAN-B of juvenile madness, which happened to be the PLAN-B that Shen Qi realized not long ago.

The two of them collided like this, and reached a certain consensus, in fact, PLAN-B is not good, or PLAN-A is better.

An old and a small game in the world is a high-end show in the eyes of outsiders, but in the eyes of Shen Qi and Academician Wu, it is just a small game.

Playing math to a certain level, there are fewer and fewer confidants, and the sense of loneliness is getting stronger and stronger. Shen Qi sighed: "Actually, I have been friends with Wu Lao Shen for a long time, and today I have the honor to learn from Wu Lao in person, and I have benefited a lot. ”

"What are your plans for coming back in the future?" Academician Wu asked.

Shen Qi nodded: "Of course, after getting a doctorate in mathematics from Princeton, I will return to China, and my roots are in China." ”

......

(This is the end of the article to ask for praise, ask for praise here)