Top Student at Their Peak
Chapter 71 - 71 65 Are You Capable

71: Chapter 65: Are You Capable?

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(Please Subscribe, Ask for Monthly Pass) 71: Chapter 65: Are You Capable?

I’ll Give a Bonus of 500,000!

(Please Subscribe, Ask for Monthly Pass) Yujiang Province, Xiao Zhou City, at Zijin West Garden not far from Zijin Campus, Professor Xue Song from the Institute of Mathematical Sciences at Yujiang University was taking a walk in the community.

As the youngest doctoral advisor at Yujiang University, and one of the youngest researchers in the “Hundred Talents Program,” the thirty-eight-year-old Professor Xue Song has a promising future ahead.

His current achievements cannot be solely attributed to a good family background.

In fact, Xue Song naturally belongs to the category of young prodigies.

After completing nine years of compulsory education domestically, his parents sent him across the ocean to enroll at Princeton International Mathematics School.

In his first year, he won the AMC 12 first prize and was invited to participate in the AIME.

After achieving outstanding scores in AIME, he also performed well in the USAMO.

Originally, in that year, he also received an invitation to join the IMO, but due to his parents’ opposition and his own fatigue from exams, he simply chose to forgo the opportunity to represent the United States in the IMO.

Yet, even so, he was directly admitted to the Princeton University School of Mathematics, where he completed his undergraduate studies in three years and caught the attention of Princeton’s renowned mathematics professor, Manjul Bhargava, becoming a student of this famous number theorist and beginning a master’s and doctoral program.

Manjul Bhargava’s primary research areas are advanced number theory and algebraic geometry, fields in which he has won the Fields Medal for his contributions.

Under this mentor, Xue Song primarily engaged in the study and research of number theory, encompassing broad topics from quadratic forms to elliptic curves.

His doctoral dissertation was on the deep results of integer distribution in number theory.

After completing his doctorate, for various reasons, Xue Song chose to return to his home country and developed his career there.

He joined Yujiang University five years ago.

Professor Xue’s abilities are indeed outstanding.

While peers were still struggling with the progression from 3+3, he directly skipped ahead twice, securing a position as an associate professor and, by virtue of a paper published in the “Mathematical Yearbook,” earned a spot in the “Hundred Talents Program.”

He is also a key talent for future development at Yujiang University and is very likely to pursue the path towards becoming an academician.

…

Mathematicians, especially those researching number theory, rarely just take walks for the sake of walking; their minds often wander to various complex thoughts.

Suddenly, his phone in his pocket started vibrating continuously.

Xue Song stopped his thoughts, took out his phone, and discovered that the WeChat group containing his graduate students had exploded, with several students @-ing him and directly discussing in the group.

“Boss, the problem you posted in the Algebra and Number Theory Tree House has been solved by that rookie!

You should go check it out!”

“Yes, boss, that rookie really solved it!

And the answer is correct, we just verified it.”

“Amazing, where is this rookie from?

It’s like some expert is using a small account to prank us!”

“Although I also think it might be some big shot joking with us, honestly, do you think those words were written by a big shot?

Plus, calling themselves ‘Little Lord’?

How embarrassing would it be if their identity were exposed!”

…

Xue Song roughly skimmed through the chat in the group, didn’t reply in the group, but turned around and headed home.

Although the phone could directly log into the forum, involving the problem he posted, using a computer was more convenient.

He knew all too well that if someone did indeed find the solution to the problem he posed, the magnitude of the solution would be considerable.

At the very least, manual calculations would be exhausting and must involve a computer.

In fact, he chose to create a stir on the forum and put forth such a problem because of a recent small breakthrough in his research.

Simply put, he discovered a method to prove that a class of equations similar to the type he posed has integer solutions.

This is also the subject of a paper he submitted to Acta Mathematica, titled “A Class of Diophantine Equations Arising from Symmetric Fractional Sums: Existence of Integer Solutions.”

The paper’s main content is proving the existence of integer solutions for a class of symmetric fractional sum-related Diophantine equations.

The equation he provided was one of the representative examples within this class of equations.

Here, it’s necessary to explain a small piece of mathematical knowledge to everyone.

In mathematics, proving the existence of an integer solution for a certain class or specific equation is not the same as directly finding its numerical solution.

The former involves using mathematical reasoning and proof techniques to analyze the equation’s structure and applying mathematical induction to confirm that there exists at least one integer solution for the class of equations.

Solving, on the other hand, involves specific calculation steps, such as using techniques like combining like terms, transposing terms, and factorization to compute the specific numerical solution of an equation.

In other words, although Xue Song has confirmed that this equation has an integer solution, he does not actually know what the numerical solution is.

The only certainty is that the numerical value is extremely large!

In fact, Diophantine equations in the field of number theory are inherently an unresolved complex issue.

For example, Fermat’s Conjecture is one of the most famous Diophantine equations, which, after being proven, became Fermat’s Last Theorem.

In 1900, at the Second International Congress of Mathematicians held in France Paris, the famous mathematician Hilbert, in his opening address, proposed a renowned list of one hundred problems, of which the tenth was concerning Diophantine equations.

The original question was: Is there a universal algorithm that can decide whether a given Diophantine equation has an integer solution?

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