From top stream to scholar
Chapter 22 Elementary Number Theory
When we arrived at the school, there was a burst of laughter from the playground.
Taking a closer look, Xu Tao was indeed playing basketball in school.There are several other girls watching.Xu Tao didn't see him either, talking and laughing with others.Yu Wanzhou shook her head, she really was a chasing boy.
When I was in the third year of high school, I knew I had a headache.Don't look at laughing happily now, there will be times when you cry in the future.
Passing by the playground, Yu Wanzhou was just about to enter the classroom.Chen Chen came towards him, looked at Yu Wanzhou and said, "Hey, why are you also at school?"
"I'm here to find the teacher." Yu Wanzhou said with a smile, "Are you also here to play basketball?"
"Not really." Chen Chen shook his head, "I'm here for tutoring, and I'll play basketball after the tutoring."
"A tutor for a math competition?"
"Yes." Chen Chen sized up Yu Wanzhou, "You also entered the preliminary examination?"
"Ah." Yu Wanzhou was quite curious about how many points Chen Chen got in the test, "How many points did you get?"
"95."
100 points out of 95, you are a top student!Yu Wanzhou stared straight at her eyes, but Chen Chen didn't care, "What's wrong? How many points did you get?"
"Me." Yu Wanzhou scratched her head, feeling that she couldn't lift her head up in front of Xueba, "I just reached the passing line."
"It's amazing." He couldn't tell what Chen Chen's original intention was. He put his hand on Yu Wanzhou's shoulder and said with a smile on his face, "Are you here to find Teacher Fang?"
"Yes." Yu Wanzhou nodded, "Hey, you also know Teacher Fang."
"Let's study math teachers. It's hard to find someone I'm not familiar with." Chen Chen's words contained a lot of information. It is estimated that this person is very popular with the teachers, so he knew almost all the math teachers in the school.
"Teacher Fang also taught us math competitions before, but now Teacher Fang doesn't teach math competitions very much." Chen Chen said regretfully, "Teacher Fang is still very good at teaching, I envy you, you can let Teacher Fang teach you."
"Do you have training classes?" Yu Wanzhou was curious.
"It's not considered a training class. As long as they can pass the first round every year, the school will pick out some good seedlings for training. But it is difficult to enter the semi-finals, and the math competition itself is difficult. Besides, none of our [-]th middle schools are really good candidates. Special students who engage in math competitions. These special students are usually gathered in key high schools, but they are just making up for it and seeking comfort."
"You participated last year, and you were also rejected in the first test?"
"Yes." Chen Chen seemed to remember something, "Right, when I took the test last year, my score was actually about the same as yours, in the [-]s. I think you have great potential, maybe next year you will be able to directly To the additional test, even to the national competition."
Yu Wanzhou is not so stupid that she can't tell what is encouragement and what is reality.He knew that Chen Chen was encouraging himself. A well-known university bully like Chen Chen didn't have confidence in the first test, let alone him.That is especially in the mathematics competition, it is impossible to do anything.
"However, this year's math competition topic is much more difficult than last year." Chen Chen explained with a smile, "Last year's topic was almost as difficult as the initial test. But this year's preliminary competition is so difficult. It was probably when Yucheng participated in the national competition last year. It must not be particularly ideal."
"Is there still such a saying?" Yu Wanzhou heard such a saying for the first time, chatting with Chen Chen while walking, "It seems that Brother Chen still has a lot of inside information."
"It's not some insider information. Anyone who pays attention to the math competition knows that last year's performance in Yucheng was indeed relatively poor, so this year's exam is relatively more difficult than last year." Chen Chen smiled bitterly, "I don't know how difficult the first exam will be. How big is it, I guess it might be simpler than last year's rematch, but it's not that simple."
Chen Chen's words can be summed up like this - everyone is having a hard time this year, and it's because last year they really stretched their hips.
After saying goodbye to him, Yu Wanzhou went directly to the office.
Because it was a holiday, there were really no other teachers in the office except Teacher Fang.Seeing Yu Wanzhou coming in, Teacher Fang greeted him warmly, "Quick, Yu Wanzhou, come here quickly."
"Hey." Yu Wanzhou came to Teacher Fang, and then Teacher Fang pointed to the seat next to him and said, "Sit down first."
"En." Yu Wanzhou sat down obediently, and listened seriously to what Teacher Fang was going to say next.
"About the mathematics competition, I don't say that you should know that it is very different from ordinary mathematics examinations. I believe you can also feel that the difference and difficulty between the usual examination papers and the mathematics competition papers is almost a geometry. The trend of rising levels."
Yu Wanzhou agrees with Teacher Fang, no matter in terms of the depth and thinking of the test, the math competition is much more difficult than the general math test.
"Basic knowledge points, the most basic things in knowledge mathematics competitions." Teacher Fang said while taking out a book, handing it to Yu Wanzhou and said, "This is elementary number theory, you should read it first."
"In mathematics competitions, number theory is the most difficult and the easiest to pass. I believe that you also have some experience and understanding."
Don't say it, I really feel it.He thought about the second question of the preliminary round, the number theory question, for a long time.I held back and didn't want to ask Teacher Fang.It's an experience in itself, and I didn't expect to be able to enter the second round.In his opinion, it's okay to pass the exam.There is no need to ask Teacher Fang because of this question. Maybe Teacher Fang will not say anything, but Yu Wanzhou is not sure what is on his mind.
He held back for a long time, but he couldn't find a good way to solve that problem.
But Teacher Fang gave him this book of number theory, no less than asking him to study number theory hard, and ask him if there is anything he doesn't understand.
"Today I am not going to explain to you the math contest questions over the years. You read number theory first, but you only have a few days. You can understand as much as you can, and then carry out targeted intensive training. Time is too tight. After the monthly exam, you will In the second round of the preliminary test, you don't have more time to study and strengthen training." Teacher Fang was still a little reconciled, and finally passed the preliminary test, but he didn't expect to be defeated in the first test.
"As for you, don't think too much. Just relax and don't be stressed. It's good to be able to pass, and it doesn't matter if you can't. The big deal is that the teacher will give you more tutoring, maybe you will be able to pass the exam next year. How about a good grade?"
Teacher Fang has already thought it over, Yu Wanzhou is indeed a good seedling.It's just that he has never been exposed to math competitions. If he starts intensive training for Yu Wanzhou from now on.Waiting to participate in the math competition next year, maybe I can really get a relatively good result in the exam.
As for this year, it must be too late.For one thing, this year's test papers are more difficult than previous years.According to experience, next year's test papers will definitely not be as difficult as this year's.Secondly, Teacher Fang is confident that as long as Yu Wanzhou is interested, he can help in the math competition to some extent.But it's just training. Compared with those teachers in key high schools, especially in the mathematics competition, there is still a big gap.
He can't make any promises to Yu Wanzhou, but Yu Wanzhou is obviously competitive in mathematics, especially in mathematics competitions.He can only do his best to tutor Yu Wanzhou. As for what he can become, that is something that Teacher Fang does not know.
Holding the elementary number theory textbook, Yu Wanzhou gnawed it abruptly.He is indeed very poor in number theory. If he doesn't have a little foundation, it will be useless to rely on teacher Fang to tutor him.What's more, Teacher Fang didn't talk about the issue of money, which means that Teacher Fang will not charge any fees for his tutoring this holiday.
He has to study hard.Teacher Fang didn't speak, and Yu Wanzhou didn't dare to give Teacher Fang money easily.
While reading the book, he was also recalling how he should do the previous number theory problem.
Yu Wanzhou wasn't talking, he was just studying quietly.Teacher Fang seemed to be calculating with something.Yu Wanzhou didn't see the above formula clearly, and it took a while.
Both parties did not speak, only the sound of 'rustling' came from the office.
Teacher Fang is doing the traditional math competition papers. He has to do it in advance first, and then select some exercises to practice for Yu Wanzhou.It is definitely impossible to practice comprehensively now, and it is necessary to practice in a targeted manner.For example, number theory, and algebra.According to Yu Wanzhou's own statement, this area may be weaker than other aspects.
In particular, the mathematics competition almost starts with plane geometry, algebra, number theory, and the analysis of solid geometry and plane geometry.
Almost all of these knowledge points are difficult, especially the many places that need to turn, which not all students in key high schools can do.Not to mention the students of ordinary high schools like Eighteenth Middle School, even more so... It's very difficult to think about it.
"Hey." Yu Wanzhou suddenly thought of something, and the other teacher said, "Teacher, you said that the second question of the paper in the preliminary round can be solved if I use Fermat's little theorem?"
Teacher Fang froze for a moment, then smiled and said, "Indeed, that problem can be solved using Fermat's little theorem."
"Mathematical induction itself is also a method in number theory." Teacher Fang was still a little confused, "You know how to use mathematical induction, so why is number theory so bad?"
Yu Wanzhou scratched her head, and said with an embarrassed smile, "I saw someone use mathematical induction before, and I remembered it in my heart. I thought it was very interesting, but I didn't expect it to be useful. I haven't studied number theory seriously before." ..."
"It's not easy." Teacher Fang handed the blank paper to Yu Wanzhou, and put the pen on the table by the way, "Do you still remember that question?"
"I still remember." Yu Wanzhou nodded, he will not forget that question.At least, not now.It was simply his nightmare.He was able to find out the answers to other questions, but that question didn't feel right no matter how he thought about it.
It was when I read elementary number theory just now, I saw Fermat's little theorem on a whim.If we use Fermat's little theorem, maybe we can solve that problem.
"Since you remember it, you can use Fermat's little theorem to do it again."
Taking a closer look, Xu Tao was indeed playing basketball in school.There are several other girls watching.Xu Tao didn't see him either, talking and laughing with others.Yu Wanzhou shook her head, she really was a chasing boy.
When I was in the third year of high school, I knew I had a headache.Don't look at laughing happily now, there will be times when you cry in the future.
Passing by the playground, Yu Wanzhou was just about to enter the classroom.Chen Chen came towards him, looked at Yu Wanzhou and said, "Hey, why are you also at school?"
"I'm here to find the teacher." Yu Wanzhou said with a smile, "Are you also here to play basketball?"
"Not really." Chen Chen shook his head, "I'm here for tutoring, and I'll play basketball after the tutoring."
"A tutor for a math competition?"
"Yes." Chen Chen sized up Yu Wanzhou, "You also entered the preliminary examination?"
"Ah." Yu Wanzhou was quite curious about how many points Chen Chen got in the test, "How many points did you get?"
"95."
100 points out of 95, you are a top student!Yu Wanzhou stared straight at her eyes, but Chen Chen didn't care, "What's wrong? How many points did you get?"
"Me." Yu Wanzhou scratched her head, feeling that she couldn't lift her head up in front of Xueba, "I just reached the passing line."
"It's amazing." He couldn't tell what Chen Chen's original intention was. He put his hand on Yu Wanzhou's shoulder and said with a smile on his face, "Are you here to find Teacher Fang?"
"Yes." Yu Wanzhou nodded, "Hey, you also know Teacher Fang."
"Let's study math teachers. It's hard to find someone I'm not familiar with." Chen Chen's words contained a lot of information. It is estimated that this person is very popular with the teachers, so he knew almost all the math teachers in the school.
"Teacher Fang also taught us math competitions before, but now Teacher Fang doesn't teach math competitions very much." Chen Chen said regretfully, "Teacher Fang is still very good at teaching, I envy you, you can let Teacher Fang teach you."
"Do you have training classes?" Yu Wanzhou was curious.
"It's not considered a training class. As long as they can pass the first round every year, the school will pick out some good seedlings for training. But it is difficult to enter the semi-finals, and the math competition itself is difficult. Besides, none of our [-]th middle schools are really good candidates. Special students who engage in math competitions. These special students are usually gathered in key high schools, but they are just making up for it and seeking comfort."
"You participated last year, and you were also rejected in the first test?"
"Yes." Chen Chen seemed to remember something, "Right, when I took the test last year, my score was actually about the same as yours, in the [-]s. I think you have great potential, maybe next year you will be able to directly To the additional test, even to the national competition."
Yu Wanzhou is not so stupid that she can't tell what is encouragement and what is reality.He knew that Chen Chen was encouraging himself. A well-known university bully like Chen Chen didn't have confidence in the first test, let alone him.That is especially in the mathematics competition, it is impossible to do anything.
"However, this year's math competition topic is much more difficult than last year." Chen Chen explained with a smile, "Last year's topic was almost as difficult as the initial test. But this year's preliminary competition is so difficult. It was probably when Yucheng participated in the national competition last year. It must not be particularly ideal."
"Is there still such a saying?" Yu Wanzhou heard such a saying for the first time, chatting with Chen Chen while walking, "It seems that Brother Chen still has a lot of inside information."
"It's not some insider information. Anyone who pays attention to the math competition knows that last year's performance in Yucheng was indeed relatively poor, so this year's exam is relatively more difficult than last year." Chen Chen smiled bitterly, "I don't know how difficult the first exam will be. How big is it, I guess it might be simpler than last year's rematch, but it's not that simple."
Chen Chen's words can be summed up like this - everyone is having a hard time this year, and it's because last year they really stretched their hips.
After saying goodbye to him, Yu Wanzhou went directly to the office.
Because it was a holiday, there were really no other teachers in the office except Teacher Fang.Seeing Yu Wanzhou coming in, Teacher Fang greeted him warmly, "Quick, Yu Wanzhou, come here quickly."
"Hey." Yu Wanzhou came to Teacher Fang, and then Teacher Fang pointed to the seat next to him and said, "Sit down first."
"En." Yu Wanzhou sat down obediently, and listened seriously to what Teacher Fang was going to say next.
"About the mathematics competition, I don't say that you should know that it is very different from ordinary mathematics examinations. I believe you can also feel that the difference and difficulty between the usual examination papers and the mathematics competition papers is almost a geometry. The trend of rising levels."
Yu Wanzhou agrees with Teacher Fang, no matter in terms of the depth and thinking of the test, the math competition is much more difficult than the general math test.
"Basic knowledge points, the most basic things in knowledge mathematics competitions." Teacher Fang said while taking out a book, handing it to Yu Wanzhou and said, "This is elementary number theory, you should read it first."
"In mathematics competitions, number theory is the most difficult and the easiest to pass. I believe that you also have some experience and understanding."
Don't say it, I really feel it.He thought about the second question of the preliminary round, the number theory question, for a long time.I held back and didn't want to ask Teacher Fang.It's an experience in itself, and I didn't expect to be able to enter the second round.In his opinion, it's okay to pass the exam.There is no need to ask Teacher Fang because of this question. Maybe Teacher Fang will not say anything, but Yu Wanzhou is not sure what is on his mind.
He held back for a long time, but he couldn't find a good way to solve that problem.
But Teacher Fang gave him this book of number theory, no less than asking him to study number theory hard, and ask him if there is anything he doesn't understand.
"Today I am not going to explain to you the math contest questions over the years. You read number theory first, but you only have a few days. You can understand as much as you can, and then carry out targeted intensive training. Time is too tight. After the monthly exam, you will In the second round of the preliminary test, you don't have more time to study and strengthen training." Teacher Fang was still a little reconciled, and finally passed the preliminary test, but he didn't expect to be defeated in the first test.
"As for you, don't think too much. Just relax and don't be stressed. It's good to be able to pass, and it doesn't matter if you can't. The big deal is that the teacher will give you more tutoring, maybe you will be able to pass the exam next year. How about a good grade?"
Teacher Fang has already thought it over, Yu Wanzhou is indeed a good seedling.It's just that he has never been exposed to math competitions. If he starts intensive training for Yu Wanzhou from now on.Waiting to participate in the math competition next year, maybe I can really get a relatively good result in the exam.
As for this year, it must be too late.For one thing, this year's test papers are more difficult than previous years.According to experience, next year's test papers will definitely not be as difficult as this year's.Secondly, Teacher Fang is confident that as long as Yu Wanzhou is interested, he can help in the math competition to some extent.But it's just training. Compared with those teachers in key high schools, especially in the mathematics competition, there is still a big gap.
He can't make any promises to Yu Wanzhou, but Yu Wanzhou is obviously competitive in mathematics, especially in mathematics competitions.He can only do his best to tutor Yu Wanzhou. As for what he can become, that is something that Teacher Fang does not know.
Holding the elementary number theory textbook, Yu Wanzhou gnawed it abruptly.He is indeed very poor in number theory. If he doesn't have a little foundation, it will be useless to rely on teacher Fang to tutor him.What's more, Teacher Fang didn't talk about the issue of money, which means that Teacher Fang will not charge any fees for his tutoring this holiday.
He has to study hard.Teacher Fang didn't speak, and Yu Wanzhou didn't dare to give Teacher Fang money easily.
While reading the book, he was also recalling how he should do the previous number theory problem.
Yu Wanzhou wasn't talking, he was just studying quietly.Teacher Fang seemed to be calculating with something.Yu Wanzhou didn't see the above formula clearly, and it took a while.
Both parties did not speak, only the sound of 'rustling' came from the office.
Teacher Fang is doing the traditional math competition papers. He has to do it in advance first, and then select some exercises to practice for Yu Wanzhou.It is definitely impossible to practice comprehensively now, and it is necessary to practice in a targeted manner.For example, number theory, and algebra.According to Yu Wanzhou's own statement, this area may be weaker than other aspects.
In particular, the mathematics competition almost starts with plane geometry, algebra, number theory, and the analysis of solid geometry and plane geometry.
Almost all of these knowledge points are difficult, especially the many places that need to turn, which not all students in key high schools can do.Not to mention the students of ordinary high schools like Eighteenth Middle School, even more so... It's very difficult to think about it.
"Hey." Yu Wanzhou suddenly thought of something, and the other teacher said, "Teacher, you said that the second question of the paper in the preliminary round can be solved if I use Fermat's little theorem?"
Teacher Fang froze for a moment, then smiled and said, "Indeed, that problem can be solved using Fermat's little theorem."
"Mathematical induction itself is also a method in number theory." Teacher Fang was still a little confused, "You know how to use mathematical induction, so why is number theory so bad?"
Yu Wanzhou scratched her head, and said with an embarrassed smile, "I saw someone use mathematical induction before, and I remembered it in my heart. I thought it was very interesting, but I didn't expect it to be useful. I haven't studied number theory seriously before." ..."
"It's not easy." Teacher Fang handed the blank paper to Yu Wanzhou, and put the pen on the table by the way, "Do you still remember that question?"
"I still remember." Yu Wanzhou nodded, he will not forget that question.At least, not now.It was simply his nightmare.He was able to find out the answers to other questions, but that question didn't feel right no matter how he thought about it.
It was when I read elementary number theory just now, I saw Fermat's little theorem on a whim.If we use Fermat's little theorem, maybe we can solve that problem.
"Since you remember it, you can use Fermat's little theorem to do it again."
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