Knock knock!

Cheng Nuo knocked on the blackboard and looked at the people in the mathematics department under the podium with a smile, "Let's continue talking." ”

"If a and a-1 are both unit roots, let b be the complex conjugation of a, and there is ab =|a|² = 1, (a-1)(b-1)=|a-1|² = 1. ”

"It can be solved that a = (1±√3i)/2, α = (1+√3i)/2, and β = (1-√3i)/2. ”

"If a-1 = 0, then a = 1. ”

"So the root of f(x) can only be 0, 1,α,β, and the root of f(x+1) can only be -1, 0,α-1,β-1......"

One formula after another was written on the blackboard by Cheng Nuo.

Whew!

Line after line of closely related mathematical formulas, for students of the Department of Mathematics at Tsinghua University, although it cannot be called a book in heaven. But it also takes time to understand.

But Cheng Nuo didn't give everyone this time to understand at all.

In the eyes of everyone, Cheng Nuo is like writing the calculation steps in his head.

Without any pause, without any hesitation, Cheng Nuo was writing on the blackboard while explaining with his mouth crackling like a cannon.

The smooth movements don't look like a freshman at all. It's more like an old teacher who has been immersed in education for many years.

Soon, the entire four blackboards were filled with two by Cheng Nuo.

But at this point, the problem is still not solved.

"Let f(x)= c·x^m· (x-1)^n, with f(x²)= c· (x²)^m· (x²-1)^n = c·x^(2m)· (x-1)^n· (x+1)^n， f(x+1)= c· (x+1)^m·x^n。 ”

"Substituting the equation yields c·x^(2m)· (x-1)^n· (x+1)^n = c²·x^(m+n)· (x-1)^n· (x+1)^m。 When c ≠ 0, the equation holds if and only if m = n, c = 1. Therefore f(x)= x^m· (x-1)^m。 ”

Finally, Cheng Nuo wrote the calculated results on the blackboard.

Therefore, only the polynomials that satisfy the conditions are 0, 1 and x^m· (x-1)^m！”

That's it, call it a day!

After writing the last stroke, Cheng Nuo smiled confidently and stunned the chalk with only the chalk head on the podium.

The audience was silent!

Bang Bang Bang ~~!

Liao Zhixing, who was standing on the side of the podium, looked at Cheng Nuo with satisfaction and appreciation, and applauded gently.

Bang Bang Bang ~~!

The students of the mathematics department in the class applauded when they saw Liao Zhixing, and they all applauded unconsciously. Except, of course, for one person.

The applause rang for a long time before it gradually stopped.

"Teacher, this is my own solution step, I don't know if it's correct, and I ask the teacher for advice. Cheng Nuo spoke in a very sincere tone.

Liao Zhixing said with a smile, "Correct! Completely correct! Cheng Nuo, whether it is your solution steps or the final answer, it can be called perfect! Anyway, I can't find any mistakes." ”

"Come, let's applaud this classmate's performance again!"

The teacher speaks, how can you not obey!

So, the classroom burst into applause again.

Cheng Nuo stood on the podium, looking helpless and flattered, he waved his hand again and again, "No, no, stop." You don't have to stop ......."

Cheng Nuo's face straightened, "I'm just solving a simple problem, and I'm not proud of it." ”

"I believe that the students here must have figured out this question earlier than me, but they were just embarrassed to raise their hands. ”

Cheng Nuo said bitterly, "However, I still hope that everyone here can behave positively." Don't twist and pinch like a flower girl. Now that you have come to Tsinghua University, you should not be lazy! Studying hard is the right way! If we don't even have the courage to speak on the stage, then how can we become a useful pillar of society?"

After speaking, Cheng Nuo let out a long sigh.

The whole class heard eight words from Cheng Nuo's sigh.

Mourn its misfortune and be angry with it!

Class: "......"

Do you think we don't want to raise our hands to answer?

But what is it...... We really haven't figured it out!

Also, you're not our classmate! Where did that no-nonsense bystander mentality come from!

On the side, after listening to Cheng Nuo's impassioned remarks, Liao's favorability towards Cheng Nuo was rising.

In this world, it is not uncommon for good students like Cheng Nuo to be seen!

The idea of wanting to focus on cultivating Cheng Nuo was like a blossom sprouting, lingering in Liao Zhixing's mind.

Three steps turned into two steps, Liao Zhi walked in front of Cheng Nuo and patted Cheng Nuo's shoulder heavily. "This classmate, that's a good point!"

Cheng Nuo smiled, "No, it's the teacher who taught you well!"

"Haha!" Liao Zhixing laughed, and nodded with relief, "You kid, you have learned to pat on the back!"

"This year, the mathematics department can produce a kid like you, it's good, it's good!"

"By the way, what's your name, I'll make a note of it, and I'll find you in the future. ”

It just so happened that Liao Zhixing had a research project in his hand, and there was still a lack of one person.

Cheng Nuo, although he is only a freshman. But from the perspective of countless people, the future of this son is limitless.

It's better to put Cheng Nuo into that research group now and exercise it. As for how much experience can be accumulated, it is entirely up to Cheng Nuo himself.

However, now that Liao Zhixing remembers, he really doesn't know the name of the student in front of him.

Cheng Nuo was most afraid of this, he hesitated to speak, "Teacher, my name is Cheng Nuo." ”

"Cheng Nuo?" I don't know why, hearing this name, Liao Zhixing has an inexplicable sense of familiarity.

However, under the podium, when Cheng Nuo reported his name, it was already a pot of porridge below.

Cheng Nuo!

This name is an indelible shadow for the college entrance examination students of the class of 2020, especially for them who are the top students of various schools.

With a high score of 730, they won the top prize in the 2020 science college entrance examination, so that these students can't afford to resist any idea.

The name Cheng Nuo, even if they are seventy or eighty, will not forget.

It's just that they heard that Cheng Nuo entered the mathematics department of the School of Management and Economics. I thought there would be no more intersections in this life.

Why...... It will appear in a high substitute classroom. I even gave a math problem to our math students.

On the podium, Liao Zhixing, who had always felt that the name Cheng Nuo was very familiar, opened his briefcase, picked up the roster, and was ready to look for Cheng Nuo's name.

On the side, when Cheng Nuo saw Liao Zhixing's movements, he knew that it was almost impossible to hide the matter anymore.

Turn yourself in, and you can still get leniency!

Cheng Nuo stiffened his head, smiled dryly, and said tentatively, "Teacher, if I say that I am not a student of the mathematics department, what will happen to you?"

Suddenly, Liao Zhixing, who was looking down at the roster, remembered it.

No wonder the name Cheng Nuo is so familiar!

Since he is a teacher at Tsinghua School of Mathematics, he pays special attention to the mathematics of the college entrance examination every year.

He remembered that only one person got a full score in the mathematics test paper of this year's college entrance examination, and that person's name was Cheng Nuo, and he was also the champion of this year's science college entrance examination!