Qiao Yu stood outside the building as usual, watching Principal Zhang and Teacher Lan out of his sight before turning to go home.
For him, doing so not only shows respect for the guests, but also costs almost nothing.
Qiao Yu's purpose is to leave a good impression on useful people rather than leave a bad impression. Of course it's nice to show your personality, but if it conflicts with the potential benefits, then don't let it go for the time being. It will only become the eyes of passers-by. The most beautiful boy can only satisfy his vain vanity.
No matter how nice a passerby's words are, they can't change his life. But the money that goes into his pocket is real good stuff. The merchant will most likely not discount the customer because of his personality, but it may break his bones because the customer is too individual. .
Qiao Yu has always felt that the biggest 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 kills a bird, the wind will destroy it. In short, personality must be the same as ability. Show it when it's time to show it, hide it when it's time to hide it.
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 run away and go home.
It was a good idea, but he was stopped by an adult: "Qiao Yu, did you just see Principal Zhang off?"
"Yeah." After saying that, Qiao Yu wanted to leave again, but was stopped again: "Wait a minute, I took out the trash, let's have a chat. I won't waste your time." Qiao Yu thought for a while, but still stood. Waiting at the gate.
The trash can for each unit is not far outside the building. Indeed, Lao Xia walked back directly without waiting for long, then skillfully took out a pack of cigarettes from his pocket, took out one and put it in his mouth. I was about to put it back in my pocket, but then I 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 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 have to quit smoking. Otherwise, he won't take me to play." Lao Xia was a little bored. .
It's not that Qiao Yu chose to quit smoking because of his daughter, but because he didn't quite understand what IMO was and was too embarrassed to ask. He just felt 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 abbreviation of International Mathematical Olympiad. There is no way, people who use Indo-European languages ​​like to make abbreviations to make people listen. "In the fog."
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 say you want to, but I am 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: "That's because Uncle Xia, you often have to work the night shift and you just need to refresh yourself. I really want to transfer you to work every day. Just stay on the train and you can quit. People's habits are all passed down."
Lao Xia smiled. This boy 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 are not good since I was a child. I was able to join the railways back then because I was in the same position as my father. I will probably be like this in my life, and I won't have much future." .
Unfortunately, this poor job is long and time-consuming, and I have to follow the car for several days. I am just such a girl, and I can’t take care of it. Fortunately, Keke is still up to date. In fact, I have to thank you. If it weren’t for you, Keke This kid probably isn’t that confident yet.”
Qiao Yu smiled politely. It was not easy for him to accept these words, especially when he could not judge the intentions of this middle-aged man.
"Now this girl doesn't even listen to what her mother and I say, she just listens to you. I'm not saying it's not good, but this girl has a bit of an awkward temperament. It's really annoying to follow her mother sometimes. If she does it in the future I've annoyed you so much, 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 a younger sister, and I will definitely take care of her as a younger sister in the future."
A smile finally appeared on the weathered face of Lao Xia, a middle-aged man. He took a last puff, flicked the cigarette butt away without any quality, then reached out and patted Qiao Yu on the shoulder: "With you, That’s all, let’s go home.”
After returning home, Qiao Yu was looked up and down strangely by Qiao Xi.
"What's wrong?" Qiao Yu asked inexplicably.
"Why do you have to stay outside for so long every time you send that good old man off?" Qiao Xi asked curiously.
"When I came back, I met Uncle Xia going downstairs to throw away the trash, so 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 hidden 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." Qiao Xi dragged her. He raised his cheeks and commented. Qiao Yu felt that his face was going to turn dark.
He knew that his mother's mind was racing, 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 Yuyi 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. , replied: "Is there a possibility that normal parents are not afraid of delaying their studies, but are afraid of causing trouble?"
This sentence clearly made my mother sitting on the sofa feel dazed for a moment.
This made Qiao Sha feel a little regretful. Just when he was about to speak, Qiao An said calmly: "It's okay. With your temperament, you definitely won't do it. Do you know what I'm most afraid of? You have a habit of calculating everything. , it’s so cold that you can’t even secrete any secretions. Are you really happy like this?”
Then, without waiting for Qiao Yu's reply, he waved his hand half-heartedly and said, "Okay, go and do your studies, and don't disturb me watching TV." Qiao Yu didn't say a word and got into his room dejectedly.
.
I feel very annoyed. I know that when I argue with my mother, he never gets the advantage, and he always talks meanly... His 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 through the defense best.
Fortunately, learning makes people happy. When a person is immersed in those beautiful number theories, all unhappiness can disappear instantly. Who said he has no hormone secretion?
Now he is very happy when doing problems every day! Once he is immersed in it, he 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. This forum was created by him unintentionally.
Found it in a search engine, hidden in a corner behind several pages.
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.
I probably learned from a website that starts with B. If you want to register for this math forum, you have to answer questions, and they are all math questions.
Although it is impossible to ask big questions due to the website registration, after all, it is difficult for the system to automatically review big questions, but the threshold of fifty multiple-choice questions in mathematics is enough to make people feel a headache. Each question is worth two points, and the score must be 90
Only if you have more than 100 points can you 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 the post titles one by one in the web interface.
So Qiao Yu spent half an hour during the day to successfully register. Then he 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 author of 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 published in the forum after review. They are all very powerful math players. For example, those like him who have just registered
Newcomers only have the title of rookie.
Not even a math rookie, just a rookie!
If you want to get the title of math 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. The big guy who happened to come up with the question was the one
He is known as a math master. 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 didn't need to think too much at all. After just one glance, he could conclude that this equation is most likely homogeneous. This means that if (a, b, c) is a special solution of the equation , then such as (7a, 7b, 7c) are its solutions. The reason is also very simple. Multiplying each variable by a constant will not change the structure of the equation. You only need the numerator and denominator learned in elementary school to eliminate this knowledge. Click and it will be taken care of.
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 looked very three-dimensional, but was actually only two-dimensional.
Yes, after this period of study, Qiao Yu has mastered the ability to restore the geometric definition of an equation in his mind. A three-dimensional equation generally defines a two-cone surface, and k n-dimensional equations are Define a d-dimensional manifold.
Specific to this question, this surface is formed by the rotation of a line passing through the origin. But at this step, after removing the denominator from the equation, Qiao Yu was a little dumbfounded. Apparently it became a cubic equation after deformation.
And it is also a cubic Diophantine equation.
Qiao Yu didn't know yet at this time 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 can be solved only by elementary mathematics. But the third-order equation involves various esoteric theories and countless problems. Open question. As for the four...
What do you say? 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 the reason why a bunch of math geeks praised the person who wrote the question. They used a seemingly simple equation to lay a big hole. It was just to give those newcomers to mathematics a little color. Well, people are actually all Much the same.
Even guys who are very good at 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 is going to get into trouble with this equation. Isn't it just about finding an integer solution?
He can definitely do it! ..
There is really nothing to say about the time that followed. The thing that worried Principal Zhang the most did not happen.
Although more and more people have come to him to ask about Qiao Yu in the past two days, the feedback is excellent - Qiao Yu really doesn't care about these garbage people who covet other people's good things every day. This also makes Zhang Tiejun completely relieved.
No matter what his character is, Qiao Yu is at least 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 to fill in the application form, no one came, so Qiao Yu entrusted Lan Jie with full authority to help him handle the matter of filling in the application form. Just like that, it was July 6th, the time to fill in the application form. At the end, Qiao Yu’s volunteer application account has not been logged in twice.
When everything was settled, Zhang Tiejun finally put his heart back into his stomach. This time he was 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 even have dreamed that such a good thing could happen to him. Of course, he had 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 fast forward this summer vacation directly to the start of the Orsay Provincial Examination League in September. It is best to fast forward
By June next year, if there is really good news that Qiao Yu won the IMO gold medal, it would be better if he got the gold medal with a perfect score.
Yes, Zhang Tiejun can't wait to see Qiao Yu represent Tie Yizhong and kill everyone. Unfortunately, time does not depend on the will of an individual.
For example, Qiao Yu, he now really 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 with the title of mathematics master actually came out and replied to him: "I will use my future mathematics to
Life is guaranteed, this question has an integer solution 100% of the time."
Below are a bunch of math geeks with various yin and yangs. 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, when I look at a question like this, my brain tells me, stop struggling! You can't solve it!"
"You are a prospective graduate student in a certain mathematics school or graduate school this year, right? Your tutor recommended you to come here? Let me tell you, this type of number theory problem that requires integer solutions is not as simple as it seems. Listen to my uncle's advice and learn real mathematics.
The first step is actually to learn to let go. Accepting the fact that you are mediocre is an inevitable process on your path to mathematics, and remembering 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 mathematical expert 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 really followed this problem
He's getting better at it. This is already the fifth day he's 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 videos. But in the evening, Qiao Yu is really
I have been struggling with this equation problem.
It was precisely because of this question that he was unable to maintain the good work and rest habits he had just developed. He accidentally thought about it until two or three in the morning. This was probably the same as the cram school that Xia Keke signed up for on July 8th.
Related to the official opening of classes.
The schedule of the cram school is similar to that of junior high school. Classes start 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 very difficult to live such a life during the summer vacation.
It's hard, but if your goal is Huaqing or Peking University, if you're not gifted, you have to persevere no matter how hard it is.
After all, in high school, there are many students who suffer more than the social beasts of 996. Not to mention that when you work in 996, you can still find time to fish and deceive the leaders. If you choose to fish in high school, you are purely deceiving yourself. It is nothing more than high school for only 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 get to the end.
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 used the desktop computer at home. He finally solved the equation at 8:30 pm on July 12th. Then he couldn't help but cursed. Voice: "Me!"
Huangtian paid off. He finally solved this stupid equation, and after taking it in for verification, the equation relationship could indeed be established. But the answer was an exaggeration.
Because the values ​​of the three variables a, b, and c all reach 80 digits! The final result is:
a=154476802108746166441951315019919837485664325669565431700026634898253202035277999 b=36875131794129999827197811565225474825 492979968971970996283137471637224634055579, 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 some 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 is 10 to 160 times Square. According to the peak computing power of a large Chinese supercomputer of 1.25 billion calculations, it can only calculate 10 to the power of 18 per second. So if you want to solve this problem, it will also take 10 to the power of 134 years.
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 draft 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 it took more than ten sleepless nights! Fortunately, no matter how tortuous the process was, He finally figured it out!
So Qiao Yu quickly logged on to the forum, and opened a new post with high spirits, bearing the title of a rookie. "That equation that you all said was difficult and impossible to solve was solved by this rookie!"
Then I quoted the original question, copied and pasted the answer directly, and simply @@the original 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. Now I will publish the answer as follows... In addition, I want to reply to some people Some previous speeches.
The senior who said that mathematics does not rely on brute force but relies on brains, thank you for the advice. It turns out that I also have a brain. But I am thinking, if you just look at it, your brain will tell you not to bother, does it mean that your brain is full? Do you feel that your IQ is not high enough, so you actively trigger the alarm to make you quit in the face of difficulties?
But I'm really sorry. When I saw this question for the first time, my brain definitely told me that the solution process of this question is as simple as its stem. As long as you are willing to solve it, You can definitely figure it out!
Now it seems that my brain was right! Oh, by the way, I also want 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 it I understand my 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 now. I'm here in this forum. You old guys will have many opportunities to get angry in the future! I'm afraid that you will be so angry now that you will ask questions in the future. It’s no use. If you are not convinced, you can continue to talk to Mr. Mathematics, and I will continue!”
After posting, Qiao Yu felt refreshed, jumped onto the bed, and fell asleep instantly.
In reality, he can only be submissive for the dozens or hundreds of red papers because of the pressure of life. On the Internet, I'm sorry, I will punch hard if I'm unhappy.
Anyway, those random netizens on the forum didn’t know him, so they wouldn’t affect him in the slightest. When it’s time to look down on people, he had to look down on them. So, as expected, Qiao Yu’s new post went viral!
Chapter completed!