Omnipotent Data

Boom!

Cheng Nuo tapped the blackboard heavily, and looked at everyone in the math department with a smile on his face, "Let's continue."

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

"It can be solved to get a=(1±√3i)/2, record α=(1+√3i)/2, β=(1-√3i)/2."

"If a-1=0, then a=1."

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

Each formula was written on the blackboard by Cheng Nuo.

Swish Swish Swish!

Line after line of closely related mathematical formulas is not a holy book for the students of Tsinghua Department of Mathematics. But it takes time to understand.

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

In the eyes of everyone, Cheng Nuo seemed to have written the calculation steps in his head.

Without any pause, without any hesitation, Cheng Nuo wrote on the blackboard while explaining like a cannonball.

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

Soon, Cheng Nuo filled two of the four blackboards.

But so far, the problem is still not solved.

"Let f(x)=c·x^m·(x-1)^n, have 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."

"Substitute into the equation to get c·x^(2m)·(x-1)^n·(x+1)^n=c2·x^(m+n)·(x-1)^n·(x+ 1)^m. When c≠0, the equality holds if and only if m=n, c=1. So f(x)=x^m·(x-1)^m."

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

"So, the only polynomials that satisfy the condition are 0, 1 and x^m·(x-1)^m!"

Done, call it a day!

After finishing the last stroke, Cheng Nuo smiled confidently and left the chalk on the desk in a daze.

The audience was silent!

Clap clap ~~!

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

Clap clap ~~!

Seeing Liao Zhixing applauding, the students of the mathematics department in the class clapped accordingly. Of course, except for one person.

The applause rang for a long time before gradually subsiding.

"Teacher, this is my own step to solve the problem. I don't know if it is correct, so I ask the teacher for advice." Cheng Nuo said in a very sincere tone.

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

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

If the teacher speaks, there is nothing wrong with it!

Then, there was another clap of applause in the classroom.

Standing on the podium, Cheng Nuo looked at a loss and was flattered. He waved his hands repeatedly, "No, no, stop. You don't need to stop..."

Cheng Nuo straightened his face, "I just solved an extremely simple problem, and I'm not something to be proud of."

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

Cheng Nuo said earnestly, "However, I still hope that everyone here can be more positive. Don't be coy and like a flower girl. Since you have come to Tsinghua University, you shouldn't be lazy! It’s the right way! If we don’t even have the courage to speak on stage, how can we become a pillar of talent useful to society?”

finished speaking,

Cheng Nuo let out a long sigh.

The whole class recognized eight characters from Cheng Nuo's sigh.

Mourn its misfortune, anger its indisputable!

all the classmates:"……"

Do you think we don't want to put our hands up?

But what the hell...we really haven't figured it out!

Also, you are not our classmate! Where did that bystander mentality that has nothing to do with me come from?

On the side, after listening to Cheng Nuo's impassioned remarks, Liao Zhixing's favorability towards Cheng Nuo gradually increased.

In this world, good students like Cheng Nuo are not uncommon!

The idea of ​​focusing on cultivating Cheng Nuo lingered in Liao Zhixing's mind like a flower sprouting.

Three steps turned into two. Liao Zhi walked up to Cheng Nuo and patted Cheng Nuo's shoulder heavily. "This classmate, well said!"

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

"Haha!" Liao Zhixing laughed, and Lao Huai nodded in relief, "You kid, you have learned how to flatter!"

"This year, the Department of Mathematics can produce a boy like you, not bad, not bad!"

"By the way, what's your name, I'll remember it, so I can find you in the future."

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

Cheng Nuo, even though he's just a freshman. But Liao Zhixing has read countless people's eyes, this son, the future is limitless.

Why don't you put Cheng Nuo in that research group now and practice it. As for how much experience he could accumulate, it was entirely up to Cheng Nuo himself.

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

Here it is, at last! This was what Cheng Nuo was most afraid of, he said hesitantly, "Teacher, my name is Cheng Nuo."

"Cheng Nuo?" For some reason, Liao Zhixing felt an inexplicable sense of familiarity when he heard this name.

However, under the podium, when Cheng Nuo announced his name, there was already a mess.

Cheng Nuo!

This name casts an indelible shadow on the 2020 college entrance examination students, especially those top students from various schools.

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

Cheng Nuo's name, even when they were seventy or eighty years old, they would not forget it.

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

But why... would it appear here? Appeared in the class of the senior substitute class. He even taught a math problem to our math department students.

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

Next to him, seeing Liao Zhixing's movements, Cheng Nuo knew that it was almost impossible to keep things hidden.

Surrender yourself, at least you can fight for clemency!

Cheng Nuo bit the bullet, smiled dryly, and asked tentatively, "Teacher, what will you do if I say that I'm not a student of the mathematics department?"

Suddenly, Liao Zhixing, who was flipping through the roster with his head down, remembered.

No wonder the name Cheng Nuo is so familiar!

Since he is a teacher at Tsinghua School of Mathematics, he is very concerned about the mathematics of the college entrance examination every year.

He remembered that only one person got full marks in the mathematics test paper of this year's college entrance examination, and that person's name was Cheng Nuo, who was also the top scorer in this year's science college entrance examination!

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