Great Country Academician

In the quiet classroom, Xu Chuan flipped through the math textbooks. Among the thick stack of books on his desk, some were borrowed from the library for the first and second grade math textbooks.

After all, too much time has passed, and he has forgotten what the textbooks look like. If he wants to read them, he has to read them from the beginning, so as not to miss some knowledge points and lose points in the exam, which will make him feel ashamed and lose his life.

A Fields Medal winner who can't get full marks in ordinary high school competitions might as well be reborn and smash his medals back home to grow sweet potatoes and raise pigs.

After more than an hour, the bell rang for the end of the lunch break, and Teacher Gong, who Song Kaiji said would be here soon, entered the classroom.

"Hello, Teacher Gong."

"Hello, Teacher Gong."

In the classroom, the students who were reading and working on the questions all greeted each other. Xu Chuan raised his head, and what caught his eyes was a man in gray and black checked wool, not tall, and wearing a pair of glasses.

Completely different from Song Kaiji's half-bald hairstyle, Gong Rihui's hair is very thick, so thick that it makes people wonder if he studied mathematics, and it is so thick that it does not meet the concept of baldness in the impression of a mathematics teacher. .

"Hello, Teacher Gong."

Xu Chuan also greeted respectfully. As a contestant who often participates in competitions, although he is not in the same subject, he still knows each other.

Don't look at Mr. Gong's bushy hair, which doesn't look like he's a math student, but he has been leading the Xingcheng No. 1 Middle School mathematics competition training team for more than ten years, and the students who have gone out from him have even won IMO gold medals .

"Is Xu Chuan here? Come on, come up and do the questions first."

Gong Rihui glanced at the classroom and saw that there were more people in the classroom at a glance. He smiled and wrote a math problem on the blackboard with his backhand, and then called Xu Chuan directly.

He naturally knew this proud boy who studied physics. Like Song Kaiji, he also felt that it was a pity that such a good young man went to study physics.

How good I am in mathematics, the foundation of all subjects!

Without mathematics, you can’t even calculate how much change you get for a dish.

"Find all pairs of positive integers (x, y) that satisfy xy=y^x-y. (^ means square)"

A math problem was written on the blackboard by Gong Rihui casually, and the white chalk was thrown on the desk. He looked at this physics genius in the audience with a smile.

Xu Chuan is no stranger to the tune of doing the questions first when entering the classroom.

Whether it's physics or mathematics, on the way to the competition, there are only two words of solving problems. He has experienced this kind of scene countless times, and he is very familiar with it without the slightest nervousness.

"Brother Chuan, come on, go up and explode your chrysanthemum, I support you!"

Beside him, Lu Tianrui, with a round face, whispered cheers.

Just as Xu Chuan stood up, he staggered suddenly when he heard the words, and barely stood up by holding on to the table.

Playing math, so perverted?

In front of the blackboard, Xu Chuan casually took out a piece of chalk from the podium. The problem posed by Mr. Gong was difficult to say the least. In fact, most high school students could solve part of it.

Just like the last major question of mathematics in the college entrance examination, the first small question is basically free and easy to solve.

But the difficulty of the following small questions increased exponentially.

The question on the blackboard is the same. In the college entrance examination, it belongs to the last one or two major questions. But in the competition, it is just a junior high school question after getting started. The test is reasonable reasoning and analysis. The ability to solve problems is more comprehensive.

It is not difficult and easy to judge, even a junior high school student can see that its first answer is (1, 1).

In front of the blackboard, Xu Chuan glanced at the topic and thought about it for a few seconds before starting directly.

"Solution: It is easy to find that x=y=1 satisfies the meaning of the question, so x=y=1 is the answer, there is a solution, and when the equation has a solution, there must be x≥y.

If x=y, then x=y=1.

If x\u003ey≥2, then 1\u0026lt;(x/y)^y=y^x-2y is obtained from x^y=y^x-y, and y|x.

Let x=ky, then k≥3, k^y=y^(k-2)y, so k=y^k-2.

Because y≥2, so y^k-2≥2^k-2, because when k≥5, y^k-2≥2^k-2\u003ek, so k=3,4.

When k=3, y=3, x=9; when k=4, y=2, x=8;

Therefore, all positive integer pairs (x, y) = (1, 1), (9, 3), (8, 2) are sought. "

The chalk under his hand did not pause at all, and in just one minute, the complete verification process was listed on the blackboard.

Gong Rihui glanced at the blackboard, nodded in satisfaction, and said, "That's right, the thinking is clear, the verification is concise, and the format is standard. It's a good seed."

"However, I want to remind you that there are some differences between Shujing and Wujing. The Wujing side will more or less involve some university knowledge, but there is basically no knowledge in the Shujing. Mathematics solves it.”

"If you have self-taught college mathematics such as advanced mathematics, try not to use it in domestic competitions, because it may lead to deduction of points for solving problems beyond the outline."

"Of course, it doesn't matter if you can break into it IMO."

Xu Chuan nodded, expressing his understanding.

In fact, the students participating in the competition, whether it is mathematics or physics, or even chemical and biological information, have basically read some college textbooks, but the depth of reading varies from person to person.

He was no exception. He basically finished reading textbooks such as advanced mathematics, mechanics, heat, electromagnetism, optics, and quantum physics that are only used in universities in the third year of high school.

If you use college mathematics to solve problems when participating in the competition, it will undoubtedly be a dimensionality reduction blow to other students who have learned less, which is unfair.

In the early years of the competition, whether it was domestic or international, it was generally forbidden to use university knowledge to answer questions, but this latter rule has relaxed a lot for other subjects except mathematics.

Like his major in physics, in recent years, IPHO has taken a lot of college knowledge. Last year, he even took a test in circuit design, which is more than a sophomore.

As for mathematics, the current IMO does not prohibit the use of university knowledge to answer questions. Instead, the question maker should design the questions to prevent candidates from using university knowledge to answer questions.

Those who can give IMO questions are all masters in mathematics. Their knowledge range is definitely much stronger than that of rookies who participated in IMO in high school. You can only use high school knowledge to solve the questions you can solve.

If in this case, you can still use the superclass knowledge to solve the problem, it doesn't matter.

Although fairness is necessary, isn't the purpose of IMO just to screen out mathematical geniuses?

Your knowledge in high school can break through the blockade of these mathematicians and professors, so there is no need to fear that you will be forced to deduct some points for your pride.

Of course, this is not to say that you don’t need to learn college mathematics if you don’t need it. On the contrary, it is still necessary to learn some college mathematics.

Because it can broaden your thinking and make it easier for you to solve problems, so as not to double your brain cells.