The top student must be diligent.

Chapter 1: The Bounty Question Outside the Corridor

"What? The question on the blackboard in the corridor has been written?"

"Ah? Is this true? Go check it out!"

Similar conversations took place in every classroom of the third grade at the Affiliated High School of University of Science and Technology of Fei City.

For a moment, the senior high school students, who had been reviewing intensively and working hard for the college entrance examination in more than three months, stopped reviewing at the same time, ran out of the classroom, and came to a corner of the corridor of the teaching building.

And in that corner, there was a small blackboard with a math problem on it.

【For a finite non-empty set H consisting of positive integers, use gcd(H) to represent the greatest common divisor of all elements in H. Prove that for any finite non-empty subset A of positive integers, ∑N∈A(-2)^|N|-1gcd(H)>0】

This small blackboard and the question on it appeared in this corner this morning. Throughout the morning, almost all the senior high school students came over to watch and try to solve this problem.

However, until today's evening study session, no one had completed this "reward".

This problem is very difficult, reaching the difficulty of a competition question. If you have not received professional training in mathematics competitions, it is basically impossible to solve this problem.

Even if you have received training for math competitions, it is impossible to solve this problem without the actual ability. Some students who have participated in math competitions and even won awards in last year's China High School Olympic Mathematics Competition said that they could not solve this problem either.

However, at this moment, the proof process of this question was written out very neatly on the small blackboard that originally only had this question on it.

And it is very short, only six lines.

"Great! It turns out this is the solution!"

"What is Pei Shu's theorem used here? I've never heard of it before."

"Ah? What's so interesting about it? Please explain it to me, I don't understand anything!"

The students who were watching were talking about it. Those who understood it were amazed, while those who didn’t were confused.

There are differences between people. It is very normal that some people can understand and some people cannot.

But at this moment, no matter whether they could understand it or not, the students present had one absolute thing in common, that is, they could not solve the problem before seeing the answer, which formed a sharp contrast with the student who solved the problem.

"It's amazing that they have come up with it right away. In this case, will he have a chance to participate in the independent enrollment of the University of Science and Technology?"

"Yes, after all, this question was asked by Professor Liu from HKUST. He said that as long as one of us can answer this question, he would be willing to give that student a chance to participate in HKUST's independent enrollment, and there is also the possibility of lowering the score for admission in the independent enrollment exam."

"This is so cool."

The senior high school students present all showed envious expressions in their eyes.

As students of USTC High School, they are of course quite familiar with China University of Science and Technology. As one of the top universities in the country and one of the C9 Alliance universities, USTC is naturally very attractive to other students except those students whose grades are basically enough to get into top universities.

If you can be admitted to USTC through independent enrollment, the difficulty will obviously be lower, and you don't have to solve this question. Then when you participate in USTC's independent enrollment, you will have a chance to be admitted with a lower score.

I believe that more than 90 percent of the students present were moved.

But the only question now is - who is the student who solved this problem?

There were only students watching at the scene, and no one stood up and said that they made it.

As for impersonation? Sorry, there's a monitor on their heads, they're not stupid.

"The teacher is here, everyone please make way."

At this moment, teachers came over from the back of the onlookers, and the students made way for them to go inside.

The leading teacher was very familiar to the students present. He was their grade director, Chen Liang. At this moment, he was all smiles and said to a middle-aged man beside him: "Professor Liu, don't forget what you said yesterday. Give the student who solved that problem a chance."

Obviously, the middle-aged man next to him was the professor from USTC, Liu Bin.

Liu Bin said with a smile: "Director Chen, I will definitely not lie to you about this matter. Based on the relationship between our two schools, the resources will definitely be biased towards you. As long as the problem is really solved, I will definitely not break my promise."

"That's fine, that's fine."

Chen Liang laughed and nodded.

For him, as the head of the grade, if he could send one more student to a school like HKUST, it would be an extra credit to him.

At this time, they finally made their way through the crowd of students and arrived in front of the small blackboard.

Liu Bin walked forward and began to look around.

He was the one who set this question. In addition to being a mathematics professor at USTC, he also has another identity, that is, a teacher in the question-setting group for the China Mathematical Competition.

He basically sets questions for China's annual Mathematical Olympiad, and he has also participated in setting questions for the IMO International Mathematical Olympiad.

So he was very clear about how difficult the question he had set was.

Otherwise, how could so many talented people in the University of Science and Technology of China High School be stumped by this question for almost a whole day?
However, what made him feel relieved was that the problem was finally solved.

And it’s still done...

Very beautiful!
It took ten lines to prove the answer to this question in the standard answer he gave, but there were only six lines on the small blackboard.

However, Pei Shu's theorem was not used in his proof.

At the same time, in the eyes of others, the most wonderful thing about this proof method is the application of Pei Shu's theorem. However, as a mathematics professor and senior question setter, Liu Bin can see another wonderful thing, which is that the place where Pei Shu's theorem is inserted is very appropriate, so it can be completed in only six lines.

Simple, clear, and... showy!

"Very good, very good."

Liu Bin nodded with satisfaction, then turned around, looked at the students present, and asked, "Which student solved this problem? You should know the reward for solving this problem. Now tell me your thinking. This reward is yours."

The students present suddenly became busy again. They turned their heads and looked around with envy, looking for students who raised their hands.

However, after a long while, no one stood up.

The scene became awkward for a time.

(End of this chapter)