Chapter 66: Shocking skills, full firepower (please subscribe, please vote)
Qiao Yu stood outside the building as usual, watching Principal Zhang and Teacher Lan out of his sight, and then turned to go home.
For him, doing so not only shows respect for the guests, but also costs almost nothing.
Qiao Yu’s aim is not to leave a bad impression when you can leave a good impression on useful people. Of course it's nice to show off your personality, but if it conflicts with potential benefits, then don't let it go for the time being.
Being the most handsome guy in the eyes of passers-by for a while can only satisfy your vain vanity.
No matter how nice the words of passers-by were, they could not change his life. But the money that goes into your pocket is real good stuff.
Businessmen will most likely not discount customers because of their personality, but they may break bones because of their personality.
Qiao Yu has always felt that the greatest advantage of a country with a long history is that the ancients have almost summarized all kinds of life experiences. For example, if a gun shoots a bird in the first place, it will be destroyed by the wind.
In short, personality must be the same as ability. Show it when it should be shown, and hide clumsiness when it should be hidden.
……
Qiao Yu just turned around and walked into the building, and happened to meet Xia Hongliang walking downstairs carrying a garbage bag.
"Uncle Xia." Qiao Yu took the initiative to call out, giving Xia Keke face, and planned to go home.
The idea was good, but he was stopped by an adult: "Qiao Yu, did you just send Principal Zhang off?"
"Yes." After saying that, Qiao Yu Yu wanted to slip away again, but then he was stopped again: "Wait a minute, I threw away the garbage, let's have a chat. I won't waste your time."
Qiao Yu thought for a while and stood at the door. Waiting at the entrance of the building.
The trash can for each unit is not far outside the building. Indeed, Lao Xia walked back directly without waiting long, then skillfully took out a pack of cigarettes from his pocket, took out one and put it in his mouth. About to put it back in his pocket, he thought of something, took out the cigarette again, knocked out half of it, and handed it over.
"Do you want it?"
Qiao Yu waved his hand and refused: "No."
"Don't pretend, I saw you had it." Lao Xia glanced He glanced at Qiao Yu and said.
Qiao Yu shook his head and said, "I'm not pretending, I did smoke before and quit last month."
"Oh? Don't say it was Keke who asked you to quit." Lao Xia couldn't help but tease.
Qiao Yu shook his head again and said: "No, it's that Teacher Lan. He said that if I want to participate in IMO, I must quit smoking. Otherwise, he will not take me to play. ”
Lao Xia is a little bored.
It’s not that Qiao Yu chose to quit smoking because of his daughter, but because he doesn’t quite understand what IMO is and is too embarrassed to ask. He just feels that young people nowadays are impetuous and have too many new words. .
Fortunately, Qiao Yu probably saw something and took the initiative to explain: "IMO is the International Mathematical Olympiad, the abbreviation of International Mathematical Olympiad. There is no way, people who use Indo-European languages like to make abbreviations, which makes people Listening to the mist.”
Lao Xia was stunned for a moment, silently put the cigarette back into his pocket, took out a lighter and lit it for himself, took two strong puffs, and then laughed at himself: "You are a ruthless person, you can quit if you tell me to quit, I'm like this I’m afraid I won’t be able to quit for the rest of my life, because I still get scolded by your Aunt Liu every day.”
Qiao Yu smiled and flattered. He finished: "That's because Uncle Xia, you often have to work the night shift and you just need to refresh yourself. If I really want to transfer you to guard the train every day, you can still quit. People's habits are all forced out."
Lao Xia smiled. This kid was still as smart as before and always spoke so nicely.
“Come on, you also know that Uncle Xia and I are a serious roughneck, and my grades were not good when I was a child. Being able to join the railway back then was in line with my father’s position, and that’s probably what I’ll be like in this life. , there is no big future.
But this is it. The work is long and long, and I have to follow the car for several days. Fortunately, Coco is still doing well. If it weren't for you, I would have to thank you. The child is probably not that confident yet.”
Qiao Yu smiled politely. It was not easy for him to answer this, especially when he couldn't judge the middle-aged man's intention.
"Now this girl doesn't really listen to what her mother and I say, she just listens to you. I'm not saying it's not good, but this girl's temperament is a bit awkward. Just follow her mother. Sometimes it's really cool. Annoying. If she bothers you in the future, give Uncle Xia some face and don’t let her get off the stage."
Lao Xia said humbly.
Qiao Yu immediately said: "Don't worry, Uncle Xia, Keke has been playing with me since she was a child. I have always regarded her as my sister, and I will definitely take care of her as my sister in the future."
Lao Xia’s picture of a middle-aged man A smile finally appeared on Sang's face. He took one last puff and flicked the cigarette butt away without any quality. Then he reached out and patted Qiao Yu on the shoulder: "As long as you say so, let's go." , go home.”
...
After returning home, Qiao Yu was looked up and down by Qiao Xi in a strange way.
"What's wrong?" Qiao Yu asked inexplicably.
"Why do you have to stay outside for so long every time you send that good man off?" Qiao Xi asked curiously.
"When I came back, I met Uncle Xia going downstairs to throw away the garbage. He pulled me to chat for a few words." Qiao Yu explained angrily.
It was a normal thing, but when Qiao Xi asked it, it felt weird, as if there was some ulterior secret between him and Teacher Lan.
"Old Xia! What can he talk to you about? Shouldn't I leave Coco to you now? I think it's a little cruel if you are only fifteen years old and have to raise two women. "Point." Qiao Xi commented, dragging her cheeks.
Qiao Yu felt like his face was going dark.
He knew that his mother's thinking was fast, but it was obviously getting worse recently.
"Comrade Qiao Xi, please face up to your family status! At my age, what normal parents fear most is their children falling in love early!" Qiao Yu said righteously.
Qiao Xi asked back: "Why do you think those parents are afraid of their children falling in love early? Aren't they just afraid of delaying their studies? So do you think falling in love early will delay your studies? You are not a normal child, why do you ask me to be a normal parent?"
Qiao Yu sneered and replied: "Is there a possibility that normal parents are not afraid of delaying their studies, but are afraid of causing trouble?"
In one sentence, it was obvious that the person sitting on the sofa was worried. Mom was in a daze for a moment.
This made Qiao Yu a little regretful. Just when he was about to make amends, Qiao Xi said calmly: "It's okay. With your cautious temperament, you will definitely not do it. Do you know what I am most afraid of? You I habitually calculate everything every day, so calm that I Your hormones are no longer secreted. Are you really happy like this?"
Then without waiting for Qiao Yu to reply, he waved his hand in a dazed manner and said, "Okay, go and do your studies. Interrupting my TV viewing.”
Qiao Yu didn't say a word and got into his room dejectedly.
I feel very annoyed, knowing that when arguing with my own mother, he never gets the advantage, and he always talks bad words...
My ability to control emotions is still a bit poor!
But you can’t blame him completely. Qiao Xi probably knows how to let him break his defense best.
Fortunately, learning makes people happy. When people are immersed in those beautiful number theories, all unpleasantness can disappear instantly.
Who said he has no hormone secretion?
Now he is very happy when doing questions every day! Once you are immersed in it, you can feel the madness of those math people.
Especially the question he prepared today, which he found on a professional mathematics forum. According to the questioner, the poster who created this post, this is a particularly interesting number theory question. .
He found this forum accidentally, hiding in a corner behind several pages of the search engine.
If it hadn’t happened that the math problem he searched for coincided with some posts in the forum, it would have been impossible to notice it.
Even the registration for this forum is different from ordinary forums.
Probably borrowed from a website that starts with B, this math forum requires you to answer questions if you want to register, and they are all math questions.
Although it is impossible to ask big questions due to website registration, after all, it is difficult for the system to automatically review big questions, but the threshold of fifty multiple-choice mathematics questions is enough to give people a headache.
A question is worth two points, and the score must be above ninety points to successfully register as a member.
And only if you successfully register as a member and log in to the forum, you can browse the content of the posts in the forum.
Otherwise, you can only browse post titles one by one in the web interface.
So it took Qiao Yu half an hour to register successfully during the day. Then I saw this pinned post.
Qiao Yu clicked in and took a look. A bunch of big guys who were known as math geeks all gave thumbs up to the poster who gave the question, and said that this question was indeed very interesting!
You must know that in this forum, the math geek represents a title that can only be obtained by answering at least 80 math questions that have been reviewed and published in the forum. They are all very capable math players.
For example, a newcomer like him who has just registered will only have the title of rookie.
Not even a math novice, just a novice!
If you want to get the title of Mathematics Novice, you must first answer a question on a help-seeking post on the forum and be given a satisfactory label by the poster.
In the forum, I got the title of math geek, and then there was only one title of math guru. This kind of top-level title can be said to be extremely rare in the forum, and it doesn't often pop up. It just so happened that the guy who came up with the question was known as a math guru.
So this seemingly simple question aroused Qiao Yu's interest early in the afternoon.
This is actually an equation that requires an integer solution.
The equation specifically looks like this:
In the first step, Qiao Yu doesn't need to think too much at all. After just one glance, he can conclude that this equation is most likely homogeneous. This means that if (a, b, c) is a special solution of the equation, then (7a, 7b, 7c) are all its solutions.
The reason is also very simple. Multiplying each variable by a constant will not change the structure of the equation. As long as the numerator and denominator learned in elementary school can eliminate this knowledge point, it can be handled.
So Qiao Yu used the method of common transfer terms to transform it into a polynomial function, added a coefficient t, and then obtained a Diophantine equation.
An equation that looks like three dimensions but is actually only two dimensions.
Yes, after this period of study, Qiao Yu has mastered the ability to restore the geometric definition of an equation in his mind when he sees it.
A three-dimensional equation generally defines a two-cone surface, while k n-dimensional equations define a d-dimensional manifold. Specifically for this question, this surface is formed by the rotation of a line passing through the origin.
But at this point, after removing the denominator from the equation, Qiao Yu was a little dumbfounded.
Obviously it became a cubic equation after deformation.
And it is also a cubic Diophantine equation.
Qiao Yu still didn’t know yet that the difficulty of solving the Diophantine equation at different times was completely different.
According to the geeks in the mathematics forum, the first-order Diophantine equation can be solved by an individual. The second-order Diophantine equation only requires elementary mathematics to find the solution, but the third-order equation involves various aspects. A profound theory and countless open questions.
As for four times...
How do you say it? At present, it is a problem that normal people are unlikely to touch.
Simply put, as the power of this type of equation increases, the difficulty does not increase linearly, but increases logarithmically.
This is probably why a bunch of math geeks praised the question maker. A seemingly simple equation was used to bury a big pit. Just to give those newcomers to mathematics a little color.
People are actually all similar.
Even guys who are very strong in mathematics still like to watch other people’s fun, especially those who are new to the industry.
Coincidentally, Qiao Yu, who feels that his understanding of number theory has changed in recent times, has decided that he will have a confrontation with this equation.
Isn't it just to find the integer solution?
He can definitely do it!
......
There is really nothing to say about the next time. The thing that worried Principal Zhang the most did not happen.
Although the number of people asking him about Qiao Yu has been increasing in the past two days, the feedback is excellent - Qiao Yu really doesn't pay attention to these garbage people who covet other people's good things every day.
This also made Zhang Tiejun completely relieved.
No matter what Qiao Yu's character is, at least he is trustworthy.
On the afternoon of July 4th, the day when the third-year junior high school students returned to school to receive guidance from their teachers in filling in their applications, Qiao Yu found no one there and entrusted Lan Jie with full authority to help him handle the matter of filling in his applications. Just like that, on July 6th, the time for filling in the volunteer application was over, and Qiao Yu's volunteer application account did not log in twice.
When everything was settled, Zhang Tiejun finally put his heart back into his stomach.
This time it is really stable!
Under his leadership, Tieyi Middle School also recruited a top student who has a chance to win the IMO gold medal.
Really, a month ago, Zhang Tiejun would not have dared to dream that such a good thing could happen to him.
Of course you have to keep a low profile at this time.
After all, Qiao Yu has not yet received his results, which makes Zhang Tiejun hope for the first time that time can pass faster. If it goes faster, it is best to skip this summer vacation and go directly to the start of the Orsay Provincial Examination League in September. , it would be best to fast forward to June next year. If there is really good news that Qiao Yu won the IMO gold medal, it would be best to get the gold medal with a perfect score.
Yes, Zhang Tiejun can't wait to see Qiao Yu killing everyone on behalf of Tie Yizhong.
It is a pity that time does not depend on the will of individual people.
For example, Qiao Yu, he now hopes that time can pass slower and give him more time.
The reason why he was so quiet during this period was not only because he had reached an agreement with the school in advance, but also because he had trouble with that seemingly simple equation.
He once suspected that this question had no integer solution at all, but when he threw this conclusion on the forum, the question maker who held the title of a great mathematician actually came out and replied to him: " I will use my future mathematical life to guarantee that this question has an integer solution 100% of the time.”
There are a bunch of math geeks with all kinds of yin and yang below.
For example:
"No way? Is there really a newcomer who gets into trouble with such a despicable question?"
"Young man, your courage is really commendable, but mathematics is not about brute force. It depends on your brain! For example, if I just look at a question like this, my brain will tell me, don’t bother!”
“This year, a certain mathematics college or research institute Are you a prospective graduate student? Did your instructor recommend you to come here? Let me tell you, this kind of number theory problem of finding integer solutions is not as simple as it seems. Listen to my uncle’s advice. The first step to learn real mathematics is to learn it first. Let go. Accepting the fact that you are mediocre is an inevitable process on your path to mathematics. Remember this is more important than anything else.”
……
Seeing these jokes, Qiao Yu became even more unconvinced.
Although he didn't quite understand how credible it was that the math master said that the future mathematical life would guarantee that this problem would have an integer solution, but since everyone thought that this problem had an integer solution, he still I really struggled with this question.
This is already the fifth day he has tried to solve this equation.
Although Qiao Yu does not spend all his time solving problems every day, he still maintains the original rhythm of watching videos in the morning, and spends the afternoon brushing up on the exercises involved in the video content, but in the evening Qiao Yu has really been struggling with this equation problem for a long time.
It was precisely because of this question that he was unable to maintain the good work and rest habits he had just developed. I accidentally thought about it until two or three in the morning.
This is probably also related to the official opening of the cram school that Xia Keke signed up for on July 8th.
The schedule of cram school is similar to that of junior high school. Class starts at 7:30 in the morning, so after the 8th, it is naturally impossible for Xia Keke to wake up Qiao Yu at 8:00 every morning for breakfast.
It is indeed hard to live this kind of life during the summer vacation, but if your goal is to go to Huaqing University or Peking University, if you are not gifted, you have to persevere no matter how hard it is.
After all, in high school, there are many students who have suffered worse than the 996 social animals. Not to mention that while working 996, you can still find time to catch fish and deceive the leaders. If you choose to fish in high school, you are just deceiving yourself.
It’s just that high school only has three years, you have expectations and you can see the end. Once you enter society, once you choose to start 996, you really don’t know how many years it will take before you are done.
It's actually the same for Qiao Yu.
Even if you go to bed at three in the morning, you must still get up at nine in the morning. After all, studying in the morning is very necessary.
In this way, Qiao Yu spent ten days, and finally with the help of the desktop computer at home, he finally solved the equation at 8:30 pm on July 12th.
Then he couldn't help but cursed: "Fuck me!"
Huangtian paid off, he finally solved this stupid equation, and after bringing it in for verification, The equality relationship of the equation can indeed be established.
But the answer is exaggerated.
Because the values of the three variables a, b, and c all reach 80 digits!
The final result is:
a=154476802108746166441951315019919837485664325669565431700026634898253202035277 999,
b=36875131794129999827197811565225474825492979968971970996283137471637224634055579,
c=4373612677928697257861252602371390152816537558161613618621437993378423467772036.
Qiao Yu finally understood how mean this question was, and how dirty the math master who gave it was really!
If he hadn’t had a computer and happened to know a little bit about programming, it would have been impossible to calculate it!
As we all know, this type of problem cannot be solved directly by using computer brute force calculations, even if two variables have been determined, because to verify the calculation of the third variable as an integer, the total number of combinations All have 10 to the 160th power.
According to the peak computing power of a Chinese large-scale supercomputer of 1.25 billion calculations, it can only calculate 10 to the 18th power per second. To solve this problem, you also need 10 to 134 Year to the second power.
So we must first find a way to solve this problem.
To solve this problem, Qiao Yu really reasoned about too many things. He used up a bunch of scratch paper just for drawing elliptic curves.
The methods I tried included bringing in special values, Euclidean algorithm, modular arithmetic, approximation and approximation, mean inequality... and spent more than ten sleepless nights!
Fortunately, no matter how tortuous the process was, he finally solved it!
So Qiao Yu quickly boarded the forum, and opened a new post with high spirits despite his title of rookie.
"That equation that you all said was difficult and impossible to solve was solved by this rookie!"
Then he quoted the original question, copied and pasted the answer directly, and simply @@the poster who asked the question.
"Okay, I admit that I was superficial before. You are right. This question does have a solution. I have found the integer solution and verified it. The answer is now announced as follows... In addition, I I want to reply to some people's previous comments.
The senior who said that mathematics is not about brute force, but relies on brains. It turns out that I also have brains. But I thought about it, so you can take a look. , your brain tells you not to bother, does it mean that your brain thinks that your IQ is not high enough, so it actively triggers the alarm to let you quit?
But I am really sorry, when I The first time I saw this question, my brain told me with certainty that the solution process of this question is as simple as its stem. As long as you are willing to solve it, you will definitely be able to solve it!
Now it seems that my brain was right! Oh, by the way, I would also like to thank the uncle who tried to tell me that the first lesson in learning mathematics is to learn to give up first! Maybe you are talking about your life experience and have accepted your own mediocrity, but obviously, your life experience does not apply to me!
Maybe what I say will make you seniors feel very angry, but please don’t be angry yet. I am here in this forum, and there will be many opportunities for you old guys to get angry in the future! I'm afraid you'll be so angry now that you won't be able to answer questions in the future.
If you are not convinced, you can continue to talk to Mr. Mathematics, and I will continue! ”
……
After posting, Qiao Yu felt refreshed, then jumped on the bed and fell asleep instantly.
In reality, for the dozens or hundreds of red papers, he could only do so because of the pressure of life.
When it comes to the Internet, I’m sorry, but I’ll hit hard if I’m unhappy.
Anyway, those random netizens on the forum are unknown to him and will not affect him at all. When you should look down on people, you have to look down on them.
So, as expected, Qiao Yu’s new post went viral!
No, it should be said that half of the Chinese number theory community is excited!
(End of this chapter)