For You, I Write; For You, I Stand Still; For You, I Do the Impossible
Mary awkwardly pulled back a few pages of the paper and said, "Don't play dumb, Jonas. I know your true level."
"No, you don't know." Jonas smiled.
Mary continued rambling, "Besides your math skills, I also know..."
"Shh." Jonas made a shushing gesture. "Knowing too much won't do you any good, will it?"
"Strange person," Mary muttered, looking down at today's written report.
At that moment, Shen Qi, carrying a stack of documents, walked into the office with Professor Muller, chatting and laughing.
"Number theory is so beautiful, and its prime numbers and Diophantine equations are the most beautiful, the most elusive, yet irresistible treasures," Professor Muller said, his eyes gleaming.
"Yes, it reminds me of my girlfriend." Shen Qi was in a very good mood today.
"You're quite the ladies' man!" Muller laughed heartily, patting Shen Qi on the shoulder. "You must let me meet your girlfriend sometime."
"There's a chance," Shen Qi said. "She's a genius in number theory and is proficient in calculation. I don't think Professor Muller would mind taking on another female student."
"If she's as good as you, I'll consider it." Muller sat down in his usual spot at the round table and said solemnly, "First, let's celebrate the birth of another new theorem in Mathematics Community. From today onwards, the Wash Conjecture will become the Wash theorem, and the prover of this new theorem is Shen Qi."
"Wow!" Jonas clapped, cheering for Shen Qi.
In fact, Jonas already knew the result last night; he just wanted to applaud.
Mary's heart tightened, and she deliberately kept a straight face, her expression icy and unsmiling, actually to hide her inner tension and unease.
"Then, Shen Qi, may I have a look at your work?" Muller asked.
"Of course." Shen Qi Proof of Diophantine Equation Wash Conjecture and the Wash conjecture to Muller, then smiled and glanced at Mary.
Mary's anus tightened again. She pretended to be indifferent as she drank her coffee, but inwardly she was filled with a desire to spy on Shen Qi's printed paper.
This paper was a gift from Shen Qi to Ou Ye. After many twists and turns and setbacks, Shen Qi finally succeeded on a beautiful night in Princeton.
That former sniper was none other than Mary.
Shen Qi dared to bring over the printed copy of the proof of the Wash Conjecture because he had uploaded the paper to arVix this morning, and the whole world would know that he was the original author of the paper.
Last night, while drinking with Jonas, Shen Qi verbally told Jonas the good news.
Just now outside the Lud Hall, Shen Qi met Professor Muller. Shen Qi verbally explained the core ideas behind the proof of the Wash Conjecture.
Professor Muller was proficient in four unparalleled skills: Mathematical Physics, Algebraic Geometry, number theory, and Group Theory. Naturally, he was very interested in Shen Qi's paper on number theory.
Professor Muller then carefully reviewed Shen Qi's formal paper to see if Shen Qi had thoroughly proven the Wash Conjecture and whether there were any loopholes.
Equations of the form a1x1^b1+a2x2^b2+... anxn^bn=c are called Diophantine equation.
This type of equation, also known as an indeterminate equation or an integer coefficient polynomial equation, was proposed by the Greek mathematician Diophantus in the 3rd century AD and is one of the oldest branches of number theory.
Diophantus was a mysterious figure; perhaps due to the passage of time, only three of his mathematical works have survived.
Very little is recorded about Diophantus's life in the History of Mathematics; the most famous account is probably his Diophantus:
"God gave him one-sixth of his childhood, then one-twelfth, and he grew a beard; then one-seventh, and he lit the candle of marriage."
"Five years later, a son was born, but the poor, belated son lived only half the life of his father before entering the cold tomb."
Four years later, he too completed his journey through life.
The author of Diophantus's epitaph is unknown, but it is certain that this friend must have been knowledgeable in mathematics.
Diophantus's epitaph is a math problem: How old was Diophantus at the time of his death?
"Oh my god, Shen Qi, you used the Gap criterion and the reduction method to ingeniously solve the problem that a quartic equation is equivalent to determining all squares in the sequence {u2k+1}." The old man Muller was suddenly filled with youthful enthusiasm, becoming more and more excited as he read Shen Qi's paper.
"I have to thank Jonas for the wine." Shen Qi refilled Jonas's coffee, expressing his gratitude. "Alcohol inspires my mathematical ideas. Of course, I don't advocate excessive drinking; just enjoy it to the fullest. Yes, I enjoy that slightly hazy feeling."
"You had already completed the proof of the Wash Conjecture before I treated you to a drink, so I have no credit for it at all, but I am still happy and proud of you, my Chinese mathematician, my Mathematics Department buddy," Jonas said modestly.
"You're wrong, Jonas. I'm talking about the last time and the time before that. Before last night, you took me to the Tiger Inn twice and got me completely drunk. The first time was with Johnnie Walker, and the second time was with Jack."
"You still remember what kind of wine you drank? You're not drunk at all!"
Jonas and Shen Qi chatted and laughed, Muller focused on reviewing the paper, occasionally praising Shen Qi.
Mary all alone, her face extremely pale.
Diophantine equation have such a long history; they are simple yet complex, and appear quite innocent and naive, being nothing more than a study of integers.
However, this innocent and adorable girl will shut you out if you don't understand her heart, remaining aloof and cold as ice, ignoring your every word.
If you master the techniques to break the spell, she will be devoted to you and stay with you faithfully for life.
Shen Qi looked out the window. At this moment, he missed his girlfriend, who was far away in the East, very much. She was innocent and cute, cold on the outside but adorable on the inside, and would occasionally wave her little fist. Her angry look was the most charming.
Ou Ye, are you alright?
This paper on Diophantine equation was written for you.
Therefore, I had to prove a new mathematical theorem to make the Wash Conjecture the Wash theorem.
Yes, I did it.
Even if it takes more than a year, it's worth it.
The main significance of Diophantine equation is to discuss the number of solutions or integer solutions of polynomials with integer coefficients f(x1, x2,..., xn)=0, and sometimes also to discuss the number of solutions of systems of equations.
Many famous Diophantine equation and the study of them have enriched and promoted the development of mathematics.
The Pythagorean theorem corresponds to a Diophantine equation: x^2 + y^2 = z^2
From the perspective of number theory, the positive integer solutions of the Pythagorean equation satisfying gcd(x, y, z)=1 can be given by a family of parameters. It is a typical curve with genus 0, providing concise and powerful theoretical support for the compilation of modern primary and secondary school mathematics textbooks.
There are theoretically infinitely many Diophantine equation. The most famous one is probably Fermat's unproven conjecture that when n≥3, the equation x^n+y^n=z^n has no integer solutions with xyz≠0.
This conjecture was so difficult that it took many great mathematicians more than three hundred years of painstaking effort for Mr. Wiles to finally prove it, thus turning "Fermat's Last Conjecture" into "Fermat's Last Theorem".
Wiles's research on this Diophantine equation directly led to the development of Algebraic Number Theory, leaving a significant mark on the History of Mathematics.
When Shen Qi won the IMO gold medal in high school, the award was presented by Professor Andrew Wiles.
Years have passed, and Professor Wiles is still teaching at Oxford.
Shen Qi then arrived at Princeton, where Professor Wiles had once fought and where he had once worked, Lud Hall.
Here, Shen Qi is doing what Wiles did back then, and it seems he has already succeeded.
(Please vote with monthly tickets! I'm still at work today, but I'll update at least three times tomorrow!)