May 17, 2024.
After May Day, Star City entered the rainy season. It has been raining for two consecutive weeks without stopping.
However, Lang Jie, director of the mathematics teaching and research group of the high school department of Star City Railway No. 1 Middle School and Olympiad coach, did not care too much about the depressing and gloomy weather. He was holding an umbrella and following two students in white school uniforms from a distance.
Here's the thing.
About ten minutes ago, after Lan Jie gave an Olympiad tutoring class to the school's top math students, he did not choose to go home for dinner because he still had a night self-study class for the sophomore rocket class in the evening.
In addition, the weather was too boring on a rainy day, so I didn’t want to eat in the cafeteria, so I simply went to a wonton noodle restaurant outside the school and had a bowl of wontons.
After finishing the wontons and just going out, I saw the two first-year students in the Osai cram school who have made the most progress recently, Lu Jia and Ma Yufei, gnawing on steamed buns together and sneaking into a small alley outside the school gate. .
Just eat two steamed buns to kill yourself when you are growing taller?!
Originally, Lan Jie wanted to stop the two boys and ask them why they were not waiting at school for self-study in the evening and why they were running outside the school, but suddenly a thought came to his mind and he thought that they were idle anyway, so he happened to finish eating. After taking a walk, I simply followed him.
So this scene happened.
Soon, Lan Jie saw two guys walking straight to an Internet cafe in the alley, and then walked in.
Oh……
This time I can catch the current situation.
Although the two children have made rapid progress recently, I'm sorry, they only have an hour and a half to eat in the evening, and they still have to go online, so they must be criticized.
Besides, this internet cafe is too much.
The banner prohibiting minors from accessing the Internet is still hanging on the door, but they dare to let these first-year high school students in casually. It is obvious that the boss lacks re-education. Lan Jie feels that it is necessary to report to the Cultural Affairs Bureau in real name.
So Teacher Lan took out her mobile phone without hesitation, turned on the video recording mode, and then followed the two of them into the Internet cafe.
…
Although the computers in the Internet cafe in the alley seemed to have just been replaced with new ones, it was still as smoky as I remembered.
Although China has already issued regulations prohibiting smoking in indoor public places, and these slogans have been posted everywhere in Internet cafes, it is obvious that such small Internet cafes have not implemented them thoroughly.
But think about it, if you dare to allow minors to surf the Internet, how can you care about whether those online smoke or not?
But what surprised Lan Jie was that after the two children entered the Internet cafe, they did not go to the bar to turn on the computer directly, but went straight to the booth in the corner of the back row of the Internet cafe.
Lan Jie hid his cell phone and walked calmly behind the two of them. He happened to hear Ma Yufei, who was resting his hand on the edge of the booth, speaking: "Brother Qiao, I'm asking you again today."
"Old rules."
"Okay, let's charge fifty, right?"
"Um!"
At this time, Lan Jie had already passed by a plane where someone was playing a game. The conversation just now aroused his curiosity, so he simply sat on an empty plane, and then saw Ma Yufei turning towards the bar. .
Soon, Lan Jie heard the sound of a member's card successfully recharging fifty yuan from the bar.
Good guy, no wonder the two of them only ate steamed buns for dinner, and all their love money was charged to someone else's card!
Lan Jie became even more angry and couldn't help but turn his head and look directly into the booth.
No, he doesn't look like a big brother, but a guy who looks younger than the two of them is playing games seriously in the booth against the computer inside.
From the profile, he looked very young, looking like a middle school student at most. At this time, the young face wearing headphones was staring at the screen, holding a lollipop in his mouth, sitting in front of a black computer next to him. Lu Jia also looked at the screen carefully and muttered in a low voice: "On the left, there is someone on the left... Hey, why did he get beaten to death like this?"
At this time, Ma Yufei had come back and blocked Lan Jie's gaze. Lan Jie only saw the guy raising his hand and making a gesture of taking off his earphones.
"Brother Qiao, it's ready."
"Read it."
"The question is as follows. Assume that positive integers a and b satisfy a2+b2 that ab+1 can divide a2+b2. Prove that (a2+b2)/(ab+1) is the square of a certain integer."
Hearing this, Lan Jie almost vomited blood. Is it because he paid for his love to help him solve the problem?
This is exactly the after-school thinking question he assigned to everyone at the end of today's Olympiad class.
It can also be said to be a very classic Olympiad question.
It may be easy to just listen to the questions, but if you try to do them, you will know that they are extremely difficult.
This question type has also appeared in the International Mathematical Olympiad before. Only two contestants got full marks for this question that year. Even many judges tried to solve the problem but failed to get full marks.
Although he has slightly transformed, the difficulty is still very high.
As a result, these two guys asked a delinquent boy who was hanging out in an Internet cafe to ask this question?
It wasn't to Lan Jie's surprise that the young man sat there deep in thought and didn't say a word for a while. After all, this question was really not that easy to solve.
After about two or three minutes like this, the young man suddenly spoke: "Show me the question again."
"Okay." Ma Yufei immediately handed over an A4 paper.
Just like this, Lang Jie watched the young man staring at the topic and thinking deeply. After a few more minutes, Lang Jie finally couldn't bear it anymore and was about to stand up and go over to find out. The young man suddenly spoke again: "Do you know about Vedic Jump?" ?」
"Vedic jump? The teacher taught the Vedic theorem today. Does this have anything to do with Vedic jump?"
"So what do I say? When you study mathematics, you must learn it and apply it flexibly. Vedic jump is to use Vedic theorem to perform infinite descent to solve problems.
First, use proof by contradiction, first assume that (a2+b2)/(ab+1) is not the square of an integer, and then assume that c and d are a set of arrays that meet the conditions, and c+d is the smallest of all arrays that meet the conditions.
Suppose c is greater than or equal to d, then c square plus d square divided by cd plus 1 equals k. Factoring can yield c square minus k, cd plus d square minus k equals zero..."
"Wait a minute, Brother Qiao, please speak slower, I can't keep up here..."
Lang Jie, who was so stunned that he didn't care about hiding his figure, stood up in a daze and walked towards the booth.
Fortunately, at this time, both Ma Yufei and Lu Jia took out paper and pen to record carefully, and did not notice the movement next to them at all.
At this time, the young guy with unknown origins had already retracted his gaze from the question and started playing the game on the screen again. It seemed to be a gun battle game...
"Okay, Brother Qiao, you continue."
"Suppose the other set of solutions to the system of two-dimensional equations is e, and directly use Vedic's theorem, e plus c equals kd..."
Lang Jie listened blankly as the guy sitting in front of the computer explained the complete solution to the problem while playing the game. It sounded like there was nothing wrong with it, but this guy seemed to like to use letters randomly when setting up unknowns.
But there’s definitely no problem with the idea!
Vedic jump plus proof by contradiction!
The two children who got perfect scores at that time both used this solution.
But things are not over yet...
Because that guy is still chattering...
"Actually, there is another geometric method. To put it bluntly, this problem is a problem of point distribution on geometric figures. Construct points and slopes on the plane, find the slope and midpoint, and use distance and ratio to prove it. But it is too troublesome to draw pictures."
"It's okay, Brother Qiao, you can also tell me, I will write it down and think about the geometric method later."
"I told you to draw a picture! And the geometric method is too troublesome to talk about. Since your teacher taught Vedic theorem today, you must still use Vedic theorem to solve the problem. But if you give me another fifty membership..."
Before Qiao Yu finished speaking, he heard two first-year high school guys beside him shout in horror almost at the same time: "Teacher Lan..." Then a strong force came from the back of his neck, and the clothes strangled his neck a little. It hurt, so I could only stand up...
Chapter completed!