The top student must be diligent

Author: Zhenglu Heming

Introduction:

What will you do when you get a BUFF that can double your learning efficiency as long as you keep learning?

Xiao Yi's answer is: Study hard!

As long as you can't learn to die, learn to die!

From small exercises to unsolved conjectures;

From outdated knowledge to theories that subvert the academic world;

…

When the existing knowledge and problems in this world cannot stop Xiao Yi from learning,

He came back to his senses and suddenly discovered:

He has stood at the pinnacle of human mind!

Chapter 1 Bounty question outside the corridor

"What? Is that question written on the blackboard in the corridor?"

"Huh? Is it true? Go and have a look!"

Conversations like this took place in various classrooms of the third grade students at the High School Affiliated to the University of Science and Technology of China in Fei City.

For a moment, the senior high school students, who were all studying intensely for the college entrance examination in more than three months, stopped reviewing at the same time, and then ran out of the classroom one after another and came to a place in the corridor of the teaching building. In the corner.

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

[For a finite non-empty set H composed of positive integers, use gcd(H) to represent the greatest common divisor of all elements in H. It is proved that: for any finite non-empty subset A of positive integers, ∑N∈A(-2 )^|N|-1gcd(H)\u003e0】

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 to watch and try to solve this question.

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

Because this question is quite difficult, it has completely reached the difficulty level of a competition question. If you have not received professional training in mathematics competitions, it is basically impossible to solve this question.

Even those who have received training in mathematics competitions will not be able to solve this problem without strength - students who have participated in mathematics competitions and even won prizes in last year's Chinese High School Olympiad Mathematics Competition said, I can't solve this question myself.

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

And it's very short, only six lines.

"Wonderful, it turns out it can be solved like this!"

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

"Ah? What's so wonderful about it? Brother, please tell me, I can't understand anything!"

Among the students who were watching, there was a lot of discussion. Those who understood it looked amazed, while those who didn't understood it looked confused.

There are differences between people. It is normal for some people to understand and others not to understand.

But at this moment, regardless of whether they understand or not, the students present have one thing in common, that is, they cannot solve this question before they see the answer. The students on this question again formed a sharp contrast.

"It's awesome. This is done. If so, will he have the opportunity to participate in the independent enrollment of HKUST?"

"Yes, after all, this question was asked by Professor Liu who came from HKUST. He said that as long as any of us can solve this question, he is willing to give that student a chance to participate in the independent admissions of HKUST, and There is also the possibility of admission with reduced scores in independent admissions exams.”

"This is so cool."

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

As students from the High School Affiliated to HKUST, they are of course very familiar with Hua Guo University of Science and Technology. As a top domestic university and one of the C9 Alliance universities, except for those students whose scores are basically stable enough to be admitted to TOP universities, HKUST is very familiar with other universities. For students, it is naturally attractive.

If you can get admitted to HKUST through independent enrollment, the difficulty level will obviously be lower, not to mention that after solving this question, you will still have the opportunity to get admission with a reduced score when you participate in HKUST's independent enrollment.

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

However, the only question now is - who is the student who asked this question?

There were only students watching on the scene, and no one came forward to say that they had made it themselves.

As for impersonation?

Sorry, there's a monitor on their head, they're not stupid.

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

At this moment, from the back of the crowd of students, teachers rushed over one after another, and the students gave way to let the teachers go inside.

The leading teacher was familiar to all the students present. He was their grade director, named Chen Liang. At this time, he was smiling and said to a middle-aged man next to him: "Professor Liu, don't forget that you taught me yesterday." That’s right, give the student who solved that question a chance.”

Obviously, the middle-aged man next to him is Liu Bin, a professor from the University of Science and Technology of China.

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 question is really solved, Then I will definitely not break my promise.”

"That's good, that's good."

Chen Liang laughed, nodded and said.

For him, the grade dean, if he can send one more of their students to a school like HKUST, he will get more credit.

At this time, they finally passed through the crowd of students and came to the small blackboard.

Liu Bin walked forward and began to look at it.

He was the one who asked this question. In addition to being a professor of mathematics at USTC, he also had another identity, that is, the teacher of the Chinese Mathematical Competition.

He basically asked questions in the Chinese Mathematical Olympiad every year, and he also participated in the IMO International Mathematical Olympiad.

So he knew very well how difficult the question he asked was.

Otherwise, how could so many talents in USTC Affiliated High School be stumped by this question for almost a day?

However, what made him more gratified was that this question was finally solved.

And it was done...

very beautifully!

In the standard answer he gave himself, it took ten lines to prove this question, but there were only six lines on this small blackboard.

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

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, but as a mathematics professor and senior question setter, Liu Bin can see another wonderful thing, that is, the insertion of Pei Shu's theorem is very appropriate, so it can be completed in just six lines.

Simple, clear, and... showy!

"Very good, very good."

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

The students present suddenly gathered again, turned their heads, and cast envious eyes around, looking for students who raised their hands.

However, until a long while later, no one stood up.

The scene was once awkward.

Chapter 2 The mysterious "math expert"

Chen Liang, the head of the grade, was waiting for the appearance of the genius student with a smile on his face, and was thinking about how to praise him later. When he saw that no student stood up for a long time, his smiling face was restrained.

He frowned, and then said: "The student who solved this problem, come out quickly, don't let Professor Liu wait for a long time, this opportunity is very rare."

As the head of the grade, Chen Liang is still a very prestigious person in the senior grade department. The students basically respect and fear him, so under normal circumstances, he said this, and the student should also come out.

However, embarrassingly, the student still did not stand up.

Everyone looked at each other.

At this time, it should be considered that the student is probably not at the scene.

Of course, there is another possibility, that is, the student who solved this problem does not like Huazhong University of Science and Technology and has a better place to go.

However, if this possibility is said, it is obviously a bit low in emotional intelligence, after all, Professor Liu is right next to him.

However, the possibility of this happening is somewhat low, because they have already informed those students who have better opportunities and are capable of solving this problem not to write this problem, leaving the opportunity to other students.

So those students probably won’t do this either.

Thinking of this, Chen Liang turned around and said to Liu Bin apologetically: "Professor Liu, the student may not be here. How about this? You go to the office to rest first, and I will adjust the surveillance here to find the student, how about it?"

However, at this time, Liu Bin shook his head, touched his chin, and then said: "No, I thought of a better way."

"I think it's probably this math expert who thinks the questions I asked are a bit simple, and then he may think that our Huazhong University of Science and Technology's math strength is not good enough, so I will ask another question, and I will put this question here tomorrow morning. Welcome that student to continue to challenge."

"Of course, other students can also try it, and the rewards I mentioned before remain unchanged."

"However, the difficulty of this question..."

Liu Bin smiled slightly, "It should be more difficult."

The students present covered their faces.

God.