I just want to be a quiet scholar

Chapter 235
In published papers, Shen Qi used PLAN-A to complete the proof of Walsh's conjecture.

Suppose (X, Y) is a solution of the equation (t+1) X^4-tY^2=1, satisfying Y>1, (x, y) is the corresponding adjoint solution, N=√x^2+y ^2t, then for a certain positive integer t0 satisfying t0∣t and t2^0≤t, P(x, y)=t0^2.

这是证明沃什猜想的核心步骤，定义r0为满足（e^2.37ε2/8）^1-r0≤∣fq∣≤（e^2.37ε2/8）^-r0的正整数，沈奇在论文中使用了PLAN-A。

在PLAN-A中，沈奇令r0=1，±B1q≠A1p以及2∣fq∣（e^2.37ε2/8）＜1。

他得到了△=K（±B1q-pA1）≠0，从而最终证明方程（t+1）X^4-tY^2=1不存在两组正整数解（Xi，Yi）（i=1，2），Y2＞Y1＞1满足∣±√-1（xi-yi√-t）/（xi+yi√-t）-X^1/4∣＜1/8。

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

This guess was proved by a 21-year-old Chinese student studying abroad.

As a result, Shen Qi has won some honors and awards, and has emerged in the Chinese and American mathematics circles.

And the bunch of mathematical symbols written by Mr. Wu just now represent PLAN-B, which is another way to prove the core steps of the Walsh conjecture.

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

In fact, Shen Qi only comprehended PLAN-B not long ago, thanks to the pressure from the Princeton Mathematics Group.

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

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

Then, Shen Qi was told that he had won the Shiingshen Chern Mathematics Prize. During this special period, he could not change the published Plan-A.

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

So, Wu always wanted to discuss PLAN-B with me, but he didn't want to explain too clearly, everything was kept silent... Shen Qi walked to the whiteboard, picked up a water-based pen and wrote:

N2≥N1^7/6t^2
After finishing writing, Shen Qi humbly asked for advice: "I would like to ask Mr. Wu for guidance."

"You are very young, but pragmatic. I like pragmatic young people." Mr. Wu smiled, wiped off Shen Qi's ≥, and gave N2 a cube.

于是沈奇的答案N2≥N1^7/6t^2变更为“N2^3空白N1^7/6t^2”。

"Mr. Wu is really skilled." Shen Qi cupped his hands in a gesture of admiration, and then said: "But Xiaosheng still has a way out."

沈奇在空白处填入≤，又在N2^3之前补充一个N1，紧接擦去N1^7/6t^2，取而代之的是54B^2t^1.5
So the latest answer becomes:

N1 N2^3≤54B^2t^1.5
"Young people have lively brains, wide thinking, and formidable future generations." Mr. Wu said with a smile, and then wrote 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 loudly, and gave a thumbs up: "I'm convinced, Xiaosheng is convinced, Mr. Wu is indeed a big dipper, and the mast and scull are wiped out in ashes while talking and laughing."

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

"There is still one strategy, which is to burn the boat." Shen Qi couldn't help admiring that the academician is indeed an academician, and his level is indeed high.

Then Shen Qi wrote down a more complicated formula:
∣（4B√-t+4A）（u+v√-t）^4-（4B√-t-4A）（u-v√-t）^4∣……=8N1^8t2^2，t2＜√t
Others in the meeting room looked contemplative, but also looked dazed.

"Hahaha!" Academician Wu laughed heartily and said, "The same goal by different routes."

"Hahaha!" Shen Qi smiled happily, and the only person who knew him was Academician Wu: "The same goal by different routes."

The two mathematicians, one old and one young, admired each other, as if they had become old friends.

The room full of people looked at me and I looked at you, afraid to speak, not knowing what to say, just thinking that this should be a high-end discussion, which is of great research value.

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

"It's really useless. It's enough to write one kind of fennel characters in fennel beans." Shen Qi wiped off 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 wipe, wipe and write, write and wipe everything, how about guessing riddles?
"Professor Sun, may I ask what happened between Shen Qi and Academician Wu?" Zhou Yu'an asked in a low voice with a strong thirst for knowledge.

"The secret must not be revealed." Sun Erxiong said mysteriously.

"Then, today's report is over. Thank you for your participation. Next, I would like to ask Academician Wu to tell us a few words." Shen Qi felt that it was almost time to end. According to the usual practice, the leader should be invited to make a concluding speech.

"Three sentences, don't be hypocritical when studying mathematics, be calm and patient, live in loneliness, learn endlessly, be cautious in your words and deeds, and end the meeting." After Wu Lao finished speaking, he left with his hands behind his hands, walked to the door and turned around and said, "Shen Qi, Come out with me."

Shen Qi nodded, and left with his hands behind his back.

There was a lot of discussion in the room.

"Shen Qi is going to get individual advice from Academician Wu." Zhou Yu'an didn't understand exactly what kind of coercion Shen Qi was pretending to be. What he could understand was that Shen Qi should be pretending to be a coward and shocked everyone.

"Shen Qi is young and promising."

"This young man is not bad, he has material, he is unassuming, and he can take it easy."

"Such a calm young man is rare these days."

"Those who can go to the Princeton Department of Mathematics for further study are really talented."

Everyone praised Shen Qi, and a new star in the Chinese mathematics circle was gradually rising.

In a corner of HKU, Academician Wu and Shen Qi communicated alone.

"I have read your paper published in the "Journal of the American Mathematical Society". Assuming a and b are positive integers, then the Diophantine equation written by Walsh has at most two sets of positive integer solutions. Shen Qi, your proof method is The most perfect, I just had a whim just now, let me talk about teenage madness." Academician Wu said.

"Thank you, Mr. Wu, for your call."

"It doesn't count as a call, I just ask you to verify an 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 man was talking about the Plan-B that caused teenage madness, which happened to be the Plan-B that Shen Qi comprehended not long ago.

The two people's thoughts collided and reached a certain consensus. In fact, Plan-B is not good, but Plan-A is better.

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

After playing mathematics to a certain level, there are fewer and fewer confidants, and the feeling of loneliness is getting stronger and stronger.Shen Qi said with emotion: "In fact, I have been friends with Mr. Wu for a long time. Today, I am fortunate to have a face-to-face discussion with Mr. Wu, and I have benefited a lot."

"What are your plans in the future, come back?" Academician Wu asked.

Shen Qi nodded: "Of course, after getting a PhD in mathematics from Princeton, I will return to China. My roots are in China."

……

(This is the building asking for praise at the end of the article, those who ask for praise come here)

(End of this chapter)