Facing the clamoring Lin Yujing, Li Zheng just smiled.

How can such a child understand his current realm?

Her thinking is still limited to shortcuts and minimalist solutions.

Although the talent is excellent, this is still only the first layer -

Apply formulas.

The second layer is to forget the formula.

Let the mind pass through, trust the horses between the images and the equations, and solve the problem elegantly.

Perhaps, Lin Yujing has touched this level through retreat and cultivation.

But it doesn't matter.

Because Li Zheng is already on the third floor.

After nearly 1,000 hours of fighting, he has woven a web of mathematics and physics.

In this mathematical net, he can shuttle to any point like an electric current.

The heavy sword has no edge, no sword and no move.

This is the magic of no trick in the world of mathematics and physics-

No formula is better than a formula.

This realm is lonely.

Because it can't be described, and others can't understand it.

Li Zheng looked at Lin Yujing, who was moving forward proudly, and also felt a kind of loneliness.

After this loneliness, there was a wave of envy.

The students are spirited, and the girls are frivolous.

So naïve, so ignorant of the heavens and the earth.

How good, how happy.

Looking at Li Zheng's father-like smile, Lin Yujing was very disgusted.

"Isn't it stupid to train in the camp...... Lin Yujing shook his head, walked straight to his seat, patted out the traditional space pencil case and kettle, and said unhurriedly, "Now, I can understand Gui Jianfeng's words." ”

Li Zheng's eyebrows tightened: "What did he say?"

"It's fine. Lin Yujing squinted at Li Zheng and waved her hand casually, "You don't understand, scum." ”

"Huh. Li Zheng was not angry, and waved his hand casually, "It's just a little rap." ”

The two of them shook their heads and entered a state of ignoring no one.

This state lasted until the third biology class.

According to the agreement with Zhu Hongbo, this is the time to go to the mathematics teaching and research group to take mathematics classes.

The two didn't say anything all the way, until they entered the office, and still no one paid attention to anyone.

Zhu Hongbo is scheming and knows the small two ...... Outsiders should not interfere in the affairs of the two little classmates.

He didn't say much, and directly asked about the progress of the two of them this week.

Li Zheng replied steadily: "Mathematics has improved slightly. ”

Lin Yujing replied more steadily: "I can't see the ceiling anymore." ”

Li Zheng laughed: "I have never seen such a brazen person. ”

Lin Yujing had a knife in his eyes: "His subordinates are defeated, and they dare to bark in the math office!"

Li Zheng's eyes froze: "Find out who is the defeated general." ”

Lin Yujing snapped his fingers: "Whoever loses the most will be." ”

"Alright, alright. Zhu Hongbo was already laughing from ear to ear, "It's just such a big thing, can you quarrel?"

"Teacher Zhu, it's not a quarrel. Li Zheng turned his head sideways and said, "It's just that now, in mathematics, I'm afraid it's difficult for me to have a common language with Lin Yujing." ”

“NotNow。 Lin Yujing chuckled and waved her hand, "Never." ”

"Good. Li Zheng's face turned pale, "I didn't want to deal with you, this is bullying." Now, you've managed to provoke me. ”

After that, he turned to look at Zhu Hongbo: "Let's talk about the real math problem, Mr. Zhu." ”

"Ah......" Zhu Hongbo hesitated, "There's no need, forget it...... With all due respect, Li Zheng, of course you have a lot of potential, but you still have a long way to go to truly surpass Lin Yujing, especially in the field of top-level problems. ”

Lin Yujing nodded, very convinced.

"Say no more, let's get out of the question. Li Zheng waved his arm and pulled out his pencil case and scratch paper, "Just right, let you re-evaluate my mathematical strength." ”

"......" Zhu Hongbo glanced at Lin Yujing, and after the latter blinked badly, he said helplessly, "Since you are so resolute, then I will make a debut." But there is a sentence that says ahead, I can't stand you making such a fuss in three days, just this time, whoever is higher is who is higher, and don't engage in this kind of competition in the future. ”

"The final word, just what I want. ”

"Hmm!"

Looking at the virtues of the two, Zhu Hongbo also raised the corners of his mouth.

The students are spirited, and the girls are frivolous.

So naïve, so ignorant of the heavens and the earth.

I'm so envious.

But.

Don't think that you can easily handle the math problems of the competition, as if the math is strong.

That's not even the beginning.

What "real mathematics" comes out of the mouth.

You people who have no reverence for mathematics.

It's time to teach a lesson.

Zhu Hongbo didn't go to the question bank at all, but raised his hand directly: "Just one question, the question is very simple, I just said directly, you can just write it down." ”

Li Zheng instantly picked up the pen.

Lin Yujing also hurriedly pulled a chair and slapped the notebook on the table to prepare for recording.

"I'll just say it once, please listen to the question. Zhu Hongbo said loudly-

[Please determine if there is a positive integer n that satisfies the following conditions:]

[n is exactly divisible by 2000 different prime numbers.] 】

[And 2 to the nth power, plus one, is divisible by n.] 】

Zhu Hongbo paused for a moment, and when he saw the two of them staring at the topic they had just written, he smiled.

"That's it, you don't have to force yourself to do it. Zhu Hongbo glanced at the bell and said, "It's five minutes and 10 o'clock, give you two hours, do it at 12 o'clock, you can give up halfway, I'll tell you the analysis of ideas." ”

After that, he pulled two large stacks of papers and started the homework.

On the other side, Lin Yujing and Li Zheng stole glances at each other almost at the same time.

After noticing the other party's sneaky glance, he lowered his head in a panic and looked at his roll.

And my heart is a little more stable-

[Fortunately, she (he) is also confused. 】

Since the other party is also confused, he is not so panicked.

Li Zheng re-examined the question.

Well, isn't this kind of problem that does not rely on formulas and theorems exactly your advantage?

The web of mathematics and science, unfold!

Math Brain, Launch!

There are no tricks to win!

After 5 minutes.

Li Zheng had smoke rising above his head and was down.

Fuck your math brain.

Fuck your web of math.

What is this?

What's the hell about this......

Prove your brother-in-law.

It's not just a complete lack of ideas.

I don't even have the idea to think of an idea.

All the questions he has done, all the problems he has encountered, have nothing to do with this question.

This inexplicable thing should be called the "XXXX conjecture", right?

It's no fun to see the wind coming, right?

There may be a chance to solve the problem.

Li Zheng couldn't help but glance at Lin Yujing again.

it!

She's writing wildly!

At this moment, Li Zheng panicked.

Don't...... She's not on the first layer?

But on the fourth floor, the fifth layer?

It is impossible to reach the third level in thousands of hours by yourself.

Even genius has a limit.

No matter how calculating Zhu Hongbo is, he will not be so shameless as to be embarrassed by a question that is impossible for high school students to have ideas.

There must be some simple and crude standard solution that has been forgotten by me......

Because I have been engaged in the connection between physics and mathematics, and neglected the basic mathematical methods.

Li Zheng held his breath, and in just three seconds, a clear routine jumped out-

Mathematical Induction!

Look at my memory, it's been useless for too long, and I've forgotten it.

However, this problem is not a simple induction, it also requires the knowledge of divisibility and perhaps algebraic deformation.

The only thing that is certain is that the requirements for ideas are much greater than calculations.

Because you can't calculate the divisibility problem of 2000 prime numbers, let alone forget it, it is impossible to write 2000 prime numbers.

Logic is the most important thing, and it is only possible to solve the problem if the logic is completely smooth, and a bunch of logical words must be used to connect in the middle, and perhaps contradictions and counterproofs must be used.

Then first of all, it is necessary to forget about the number 2000.

Obviously, this is just a figure made up by the person who made the question, and it is meaningless in itself.

23333 is also OK, 666 is also OK, what is happy to write.

Exactly divisible by 2000 different prime numbers, it's just a smoke bomb.

What is actually to be proved is that it happens to be divisible by any number of primes that are different from each other.

Hmph, but that's it.

So, let's get started.

……

An hour later.

Zhu Hongbo finished the papers of the three classes.

Take a look to the left first.

Li Zheng stopped writing and writing, obviously his brain was still messed up, and he was bumping into it.

Look to the right again.

Lin Yujing simply looked at the question in a daze.

After she had written a few lines in her notebook, there was nothing more.

Zhu Hongbo smiled.

Happy?

Real math?

Isn't it cool?

Zhu Hongbo got up with a smile, picked up the thermos cup and said, "It's time to go to the bathroom, you should drink water." ”

No one paid any attention to him.

He didn't say anything more, so he went out to fetch water, and by the way, he wandered around a lot, went to chat with Tang Zhifei, and then went to talk to Tao Feifei.

When the two sides talked, the words they said were not too much.

"Guess what, they've already been stopped. ”

"Teacher Tao, don't panic, they are only high school students in mathematics, and I surrendered with a random question. ”

"Don't worry, I'm here safe. ”

"Let them know that they have to be in awe of the subject and the teacher. ”

"Hey, it's over, it's over, it's just the natural depth of math problems. ”

After a circle, Zhu Hongbo returned to the door of the teaching and research group full of spirits.

I wanted to go straight in.

But if you think about it carefully, these two people, the opportunity to be so anxious is really rare.

He secretly opened a crack in the door and peeked in.

This glimpse is a staring eye.

Outrageous!

These two people are not in a hurry at all.

It's a head-to-ear exchange!

In fact, as soon as Zhu Hongbo left, the conversation had already begun.

First of all, Li Zheng pretended to talk to himself.

"Lao Zhu asked this question...... It's a heart, isn't it......"

"Hmm......" Lin Yujing sent a response that was not a response.

After Li Zheng struggled for a while, he pulled the chair in a tangled manner: "Do you want to unite it?"

"......" Lin Yujing was also entangled for a moment, and then nodded with a "hmm".

After that, the two got closer and closer until they got together.

Muttering, endlessly.

"Yes, first prove the lemma, and then prove the more general proposition. ”

"Hmm...... The big idea, the middle counter-evidence and contradictory part, I thought about it as soon as I came up, but I couldn't find a suitable algebraic variant. ”

"I have this, look at this identity......"

"!! is really a scumbag suitable for stupid mechanical calculations!!"

"Mao, I thought of this as soon as I came up, it is the intuition of the mathematical brain. ”

"Scum, this is out, and it turns out to be super simple later. ”

"Really...... Oh, that's it, an opportunistic lazy woman. ”

"Scum, pinch you!"

"Am I wrong? Aren't you opportunistic?"

“……”

"Aren't you lazy?"

“……”

"Aren't you a woman?"

“…… I've proven all the lies you have. ”

"Damn...... Wait for me...... We hand over together, and we put it between us in advance, and we are consistent with the outside world. ”

"Hmm, scared Zhu Zhu to death. ”

After the two decided on the strategy, they rushed back to their original positions with their chairs before Zhu Hongbo returned.

Of course, Zhu Hongbo witnessed the process in the second half of the process.

By this time, his eyes were bloodshot.

Isn't that what the hell you're going to compete with?

How is it unanimous to the outside world?

At this moment, Zhu Hongbo realized.

Small two...... Two young classmates fight, the best way to persuade the fight.

It is to become their common enemy.

Zhu Hongbo was going to push the door directly in.

But looking at the virtue of the two, he just sighed, and slipped back to the corridor with the thermos cup in his backhand, all the way to the window.

Able to use mathematical methods to move forward side by side with the same enemy......

Isn't that a great blessing?

While Zhu Hongbo felt nostalgic, he was a little inexplicably sour.

After all, when his wife takes away her salary...... That's not even a bit of math to talk about......

It's hard to imagine that a 40-year-old man can be sour.

Zhu Hongbo raised his arm and looked at his watch, trying to swallow the sour taste.

There is also a limit to the beauty of adults, give them another 5 minutes.

After all, even if it's 50 minutes, 500 minutes, the result is still the same.

Impossible, this problem, they can't solve it.

Five minutes later, Zhu Hongbo pushed open the office door.

Li Zheng and Lin Yujing exchanged a small look, and then got up at the same time.

"It's done. ”

"Hmm. ”

"Hmph. Zhu Hongbo only replied with a sneer, and didn't care about the kitten between them.

He took their answers, walked over to the table, and laid them out side by side.

The left and right sheets of paper are examined line by line at the same time.

It's pretty much the same.

Well......

Let's prove a lemma first, this step is correct, but I guess this step is right.

And then there are the assumptions...... The assumption was correct.

And then there'......

Wait a minute......

They can all pinch out this identity??

This is followed by turns, variations, contradictory counter-evidence......

Then, the lemma is extended to prove a general proposition that has universal applicability.

Eventually, the existence of N was proven.

In just one minute, Zhu Hongbo completed the marking.

You don't have to look at it a second time, the idea is clearly written.

Then, beads of sweat the size of beans dripped down.

His face trembled.

This TMD ......

It doesn't make sense......

Behind Zhu Hongbo's trembling back, Li Zheng and Lin Yujing invariably exchanged small glances.

Comfortable.

The heart of awe does not exist.

After a long period of self-doubt, Zhu Hongbo stared at the two rolls and said in a trembling voice: "You...... You two...... Tell me the truth...... Have you found the answer?"

The two of them were stunned, and in the face of this, they were naturally a little weak-hearted.

Li Zheng lowered his head and said, "Tell you the truth, Teacher Zhu...... I looked at Lin Yujing's train of thought. ”

Lin Yujing also said: "I used Li Zheng's identity......"

"What about other than this?" Zhu Hongbo glared and asked more and more tremblingly, "Have you looked for this question on the Internet? Have you seen it before? Have you obtained ideas from places other than you?"

They both shook their heads at the same time.

"Holy. Zhu Hongbo burst into a foul language and sat down on the chair, "You two...... It's too much......"

"It's not that hard. Li Zheng scratched his head.

"Isn't it just an identity? Lin Yujing also felt that Zhu Hongbo had overreacted.

". Zhu Hongbo scolded again, and then picked up two answers and said angrily, "Do you know what kind of question this is? Only 35% of IMO players have made this question!"

Both opened their mouths at the same time.

IMO, International Mathematical Olympiad.

This is undoubtedly the biggest and most prestigious math competition.

Good you Zhu Hongbo!

Use this kind of thing to bully people!

The number competition is undoubtedly going to be engaged, but it is still in the very basic preparation stage, and the IMO real question will be on the IMO at this time, Lao Zhu, you are really ruthless!

However, this hatred has passed.

Only then did they understand that Zhu Hongbo's trembling was not because of annoyance, but because of excitement.

It's really exciting to be able to solve IMO problems with very limited training

But Li Zheng and Lin Yujing are far less excited than Zhu Hongbo.

"There's nothing to be happy about, I'm still far behind......," Li Zheng clenched his fists and said, "I can't do it alone, for more than an hour, even the big ideas are a mess." ”

Lin Yujing also lowered her head: "I haven't been able to find that identity either, I don't have enough time, I can't do this problem." ”

"It's just where it is. Zhu Hongbo got up excitedly, grabbed the shoulders of the two and said, "I only realized now, the advantages of the two of you are completely complementary, one is a strategist and the other is a practitioner." One is stronger than unconventional thinking, and the other is stronger than unconventional computing. If possible...... It's just possible...... The two of you must not be separated in the future!

Zhu Hongbo was too violent, causing both of them to shrink back.

After Zhu Hongbo was excited, he also knew that he had lost his words: "I ...... I'm talking about projects working together, not the kind of together. Of course, it's okay for you to be together...... Ha ha...... Hahaha......"

"Knock knock".

There was a knock on the door.

Tang Zhifei and Tao Feifei suddenly appeared at the door.

"Teacher Zhu, please come out and talk. Tang Zhifei hooked his hand.

Tao Feifei hid her face and snickered: "Hmm...... It's really stable...... Mathematics really has a natural depth. ”