My Identity As A Schoolmaster Has Been Exposed

All eyes were focused on Xu Cong, how much imagination it was to express their shock at the moment.

I can't write about their shock. Let's solve it by your own brain. It is really unimaginable.

Xu Cong knows that these people are generally shocked and generally don't believe it, but now it's a showdown, and he has nothing to hide!

In order to avoid the students from those two provinces continue to be persistent on the topic of the Olympiad, Xu Cong can only do this.

So he slowly got up, Xu Cong calmly came to the blackboard in all eyes and picked up the chalk.

Rustle... rustle...

He wrote the answer directly!

Solution: If the polynomials f(x) and g(x) have the same value when x=-2 and -5, they are written as f(x)=g(x), such as x2+7x+10=0.

When n∈{0,1,,9}, the constant n is the polynomial Q(x) that satisfies the requirements.

When n=10, Q(x)=x3+6x2+3x meets the requirements, which is abbreviated as (0, 3, 6, 1).

Generally, Q(x)=akxk++a0 is abbreviated as (a0, a1,, ak).

Suppose Q(x)=(a0,a1,,ak) and the coefficient ∈{0,1,2,,9}, we prove that there is a polynomial P(x), and the coefficient ∈{0,1,2,9}, and P(x)=Q(x)+1, the sum of coefficients of P(x) is also equal to the sum of coefficients of Q(x)+1.

Xu Cong's answer process is very slow, very slow, and the words and numbers are also very beautiful.

The regular script he used, one stroke by one stroke, gave people the feeling, like a work of art! Very pleasing to the eye!

With eloquence, Xu Cong wrote a lot on the blackboard.

His fonts are extremely ornamental, and they sink into it at a glance.

Everyone enjoyed it very much, and suddenly forgot to read the specific content on the blackboard.

What they are looking at is not the idea of ​​solving this problem, but the calligraphy of Xu Cong!

When words or numbers appear in their eyes, they feel more comfortable.

How often do you encounter this kind of visual feast?

On the blackboard at the moment:

The last step uses 10+7x+×2=0.

On the other hand, if the coefficients of Q(x)=(a0, a1,, ak) ∈ {0, 1, 2, 9}, it can be proved that there is a polynomial R(x), and the coefficients ∈ {0, 1, 2, 9 }, and R(x)=Q(x)-1.

This just needs to pay attention to Q(x)-I=Q(x)+(9,7,1) and then use the above result about Q(x)+1 many times.

From Q(-2)-Q1(-2)=0 we get 2|b₀|,

In the same way, we can get 5|b0, so 10|b0｜……

But |b₁₀=0, so b₀=0.

So bk(-2)k++b1(-2)=0, thus 22|2b1, 2|b1. Similarly 5b1. So b1=O.

By analogy, b2=bk=0 can be obtained. Therefore, the qualified Q(x) is unique.

At this point, Xu Cong turned around and looked at everyone, because he had finished writing!

The four-open blackboard was full of writing at this time, and Xu Cong didn't say a word from beginning to end.

After writing, he put down the chalk and went back, everyone was stunned!

They didn't react for a while, and they were all overwhelmed by the font on the blackboard and various solutions.

Gradually, someone murmured: "Is it really his problem? How else did he know the answer?"

Even the leaders of the education department discussed with the professors of Jingyun University. Even though they usually have high morals, but now they have encountered the evildoer Xu Cong, they have to take it seriously.

"Professor, look at this question..."

The professor ignored him, still staring at the blackboard intently, and at the same time he said to himself: "The words are really good...hiss! Ah... sorry, I lost my mind for a while, let me take a closer look!"

In the end, the proof process written by Xu Cong on the blackboard was passed by everyone with a raised hand.

Even the top professors in the country can't find any problems after reading them carefully. How can this professor find out?

But to be cautious. The professor used his mobile phone to take pictures of all the problem-solving processes.

Then he said to everyone: "Ahem! I'll go out a little bit!"

He is looking for colleagues in the industry, and his brothers come to see these questions and answers.

When the question and the idea of ​​solving the problem were sent, the other party directly called and asked: "This is the final question of the Olympiad. Where did you see it? Did someone at Jingyun University solve this problem? "

The professor immediately told him about Xu Cong: "This is not a three-province mathematics exchange meeting! One of our students came up and wrote the answer."

When the other party heard that this question was actually made by a sophomore in high school, he was startled and asked hurriedly, "What is this person's name?"

"Xu Cong!"

After the other party heard that it was Xu Cong, he breathed a sigh of relief, and returned to his calm look, and said to him lightly: "That's fine, it's all his questions, and people answer them by themselves. What's the fuss?"

My own question!

Answer it yourself!

No fuss!

It's weird if you can't write it!

But he is only sophomore in high school! Just a teenage student!

"Brother, but this student Xu Cong?" The professor still didn't want to believe it.

After hearing his doubts, the other party smiled and continued to say to him: "You can't believe it, do you? When I first came to our question group, I couldn't believe it! But getting along, this little guy has unlimited potential! "

"To be honest, if it weren't for us to stop him, his topic would be even more difficult! And it's not a super-class one!"

"You say you are not angry!"

"This Olympiad competition is difficult for many people! But where do they know, we have already won a lot of space for them!"

"Otherwise, the first and second place will really fail, even between thirty and fifty minutes!"

The professor from Jingyun University took a cold breath while listening to his brother's words.

After understanding everything, he quickly walked back and the leaders of the education department gave feedback on the situation.

moment!

The leader immediately turned his head and looked at Xu Cong. He stared at Xu Cong, his eyes filled with shock.

In this exchange meeting, even though the two provinces of the other side had a third place, and there was a group second, but compared with the person who made the paper, what is it?

The same is a sophomore!

The same classmates!

But this gap is not even a star and a half.

Looking at Xu Cong, the leader seemed to have seen the scene where Xu Cong was alone, killing thousands of troops in seconds.

With Xu Cong's participation, the meaning of this exchange meeting disappeared from this moment on.

Even the leaders of the education department couldn't help but murmured, "If we knew this would happen, what kind of exchange meeting would be held! Hasty!"

The Mathematical Olympiad was not led by the education department, and when Zhu Tiesen invited Xu Cong, he went directly!

No one else knew about this matter except for the province, the city, and Xiling High School.

Although it passed the Provincial Education Bureau, the Provincial Education Bureau and Zhu Tiesen reached certain promises verbally, and they naturally wouldn't publicize it.

So the fact that Xu Cong became the examiner of the Olympiad was kept secret by the province.

Not even the highest education department knows about it, let alone other provinces. This is also a kind of protection for the author of the question and prevents some students from retaliating.

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