Xueba's Black Technology Simulator

Gu Rou has more study materials than Lu Xiao, including freshman math.

After taking the freshman math book, after more than ten minutes of reading, Lu Xiao finished it.

Gu Rou's eyes widened, and she asked in doubt, "Have you learned it?"

"No." Lu Xiao shook his head.

"Then why didn't you watch it?" Gu Rou was puzzled.

"I'm reminiscing." Lu Xiao laughed.

Without explaining, he continued to ask Gu Rou to give him the Mathematical Olympiad test paper, and he wanted to brush up the questions.

All afternoon, Gu Rou was struggling.

I don't know if Lu Xiao pretended to be like this in front of her on purpose.

It doesn't matter if you pretend to be in front of the little girl and don't get the attention of the whole class.

Anyway, Lu Xiao didn't explain.

It was the last class, which happened to be mathematics, and Teacher Liu was preparing to go back to the office with his textbooks in his arms.

The students who will participate in the Mathematical Olympiad will come to him to study. This year, he will take everyone to participate in the Mathematical Olympiad Competition of the Experimental Middle School.

At this time, Lu Xiao came over and said with a smile, "Ms. Liu, I want to sign up for the Mathematical Olympiad."

"You!" Teacher Liu looked at the honest child in his memory in surprise.

The child used to tremble when speaking in front of him, but now it's a little different.

Lu Xiao has recently become an Internet celebrity, and he is still clear about it.

Did the kid become more confident after becoming an Internet celebrity?

Teacher Liu said with a gentle smile: "Olympiad is a bit difficult, and your strength is not so good. You are already in the third year of high school."

"Teacher, give me a chance. If you don't believe me, give me the Olympiad test paper." Lu Xiao said very confidently.

He didn't waste any time this afternoon.

He absorbed all the mathematics in the freshman year, and the mathematics experience value rose to 50/1000 for the first level.

I don't know the experience of how to calculate the black technology simulator of the rise of the great powers. Anyway, after reading a book, I feel that I have more experience than the entire high school mathematics experience.

Most importantly, he found that the Mathematical Olympiad test papers he got from Gu Rou basically didn't get stuck.

All can be smoothly simulated to get the answer.

That's why I have the confidence to let Mr. Liu test him.

Liu Yong didn't refuse anymore, so let's make a test paper and let Lu Xiao quit.

Gu Rou also followed at this time, and she also went to the math teacher's office to take the test, so that she could ask the teacher immediately if she encountered any problems.

There are still a few days left for the city entrance exam, followed by the provincial entrance exam.

One in the morning and one in the afternoon, both in Dayuan City, the capital city of the province.

There were already three students from other classes waiting in the office, all of whom were top 10 students in their grade.

Now a different species has mixed in with this group of people.

In the last exam, Lu Xiao ranked 353rd in the whole grade with a total score of nearly 700 high school seniors.

Mathematics single subject scores are estimated to be outside the 400th place.

Mr. Liu's persuasion to Lu Xiao not to sign up was not indiscriminate.

If you are not strong enough, if you insist on participating, you will even doubt your IQ in the end.

If self-confidence is hit, the college entrance examination may be affected.

Teacher Liu is not very willing to bring Lu Xiao to participate in the competition.

Lu Xiao didn't have time to say hello to the other top students, so he sat at the empty desk and waited for Teacher Liu's assessment.

Soon Teacher Liu brought a test paper, Lu Xiao shook his head and said, "I've done this one."

After speaking, he pointed at Gu Rou.

Liu Yong also looked over, and Gu Rou blushed a little, because this test paper was originally left for them by Teacher Liu, but now it was done by Lu Xiao.

After glaring at Lu Xiao, Gu Rou nodded and said, "Lu Xiao is very good, and he has solved all the big problems at the end."

Liu Yong is serious now, is it really a good seed, he didn't see it before.

He didn't look for the test paper, so he wrote a question on the draft paper.

In the acute triangle ABC, the height CE on AB and the height BD on AC intersect at point H, the circle with DE as the diameter intersects AB, AC at F and G respectively, FG and AH intersect at point K, known BC=25, BD=20, BE=7, find the length of AK.

"Teacher, where's the picture?" Lu Xiao asked.

Liu Yong also wanted to give Lu Xiao a bad start, and said with a smile, "Let's see if we can do it like this."

This requires a lot of spatial imagination, and Lu Xiao is not sure whether the simulator can answer it.

Anyway, relying on himself is a bit difficult.

Fortunately, Goldfinger never disappoints. This question is high school knowledge.

There is a detailed proof process in the simulator, but since the teacher didn't draw any pictures, he didn't bother to write the process, and it only took a few seconds to write it on paper.

prove:

AK=8.64!

In fact, if you write a proof, the entire paper will be filled. The actual answer is 216/25, which is 8.64.

"Eh!" Liu Yong wanted to say a few words of relief.

Then draw a picture, if Lu Xiao still can't make it, let Gu Rou try.

This question is a bit difficult.

Even Gu Rou might not be able to do it.

Then he can let other people do it, and if they can't do it, he will explain it in detail.

At that time, Lu Xiao knew that with his strength, he was not qualified to participate in the competition.

Now, his words were stuck in his throat.

After a while he reacted, "You did!"

"No, no, this is a question I made up just now. You can't do it, you, you." Liu Yong was tongue-tied, and soon became excited.

Gu Rou made up her mind in despair: "Lu Xiao spent more than ten minutes reading freshman mathematics, and will do very difficult Mathematical Olympiad questions in the afternoon."

After many verifications, Gu Rou has confirmed that Lu Xiao is a master of hiding. Last week, he was flipping through the book in class, and he was endorsing it.

This makes Gu Rou, who considers herself a genius, to bow down.

"It's unbelievable! It's only been a few seconds, how did you get the answer? You know, the proof process is very complicated!" Liu Yong was still muttering to himself.

Then he quickly wrote another question and said, "Try again!"

The question he wrote this time was not simple. It was the legendary sixth question, which stumped Tao Zhexuan in the 1988 math competition.

The average score of the 268 contestants on this question was only 0.6.

The four number theory experts in the arena couldn't do it in a short time.

He felt that Lu Xiao probably wouldn't be able to do it, and if he could, he must have been in contact with it before.

After he finished writing, he asked, "Have you ever done it?"

Lu Xiao shook his head honestly.

Then start reading the questions, [Positive integers a and b make ab+1 divisible a+b, prove: (a+b)/(ab+1) is the square of a certain positive integer. 】

[During the simulation, the simulation is successful and takes 3s. The problem-solving process: According to (1), a2 must be an integer;

According to (2), a2 cannot be 0;

Since a1≥b1, a2 must be less than a1

But since a1 is already the minimum solution of the equation, a2 should not be less than a1, because this is contradictory to what we say that a1+b1 is the minimum sum of the equation solutions...

So finally we can prove that (a+b)/(ab+1) is the square of some positive integer. 】

In the simulator results, several solutions are given for this question.

In order to pass the customs directly, Lu Xiao continued to write.

In fact, the knowledge points used are still high school knowledge, but very clever.

Incorporates the concept of "Vedas jumping".

In addition to the "Vedas Jump", it also involves the "Infinite Descending Method", which is also high school knowledge.

This method was first used by the great mathematician Fermat.

Based on this, he proved that the fourth power of x + the fourth power of y = the fourth power of z has no positive integer solution, which is the case of n=4 in Fermat's last theorem.

Euler also used the method of infinite descent to prove that every prime number with a remainder of 1 after division by 4 can be expressed as the sum of two squares.

It is worth mentioning that this theorem was also first proposed by Fermat, although he did not provide a proof.

Since it is the knowledge of high school knowledge points, it is within the range that the simulator can perfectly simulate.

Lu Xiao directly proved it indirectly.

He found that the manuscripts were completely insufficient.

The math teacher quickly took out a large stack of manuscripts to write the proof process for Lu Xiao.

He could see that Lu Xiao had never been exposed to this problem before. During the proof process, he also deduced other proofs. This is simply what mathematicians can do!

Now, is Lu Xiao already at this level?

Reminiscent of the question that Lu Xiao proved that he took out before, it only took a few seconds to get the answer.

This performance is somewhat similar to Ramanujan in history.

Ramanujan gave the answer directly from the brain without any calculation process at all. This is a special talent.

Liu Yong has a bold idea!

If you put one of the seven major problems of the millennium in front of Lu Xiao.

He won't prove such a difficult question!