91. The first number theory class(1/2)
Knowing what dishes are the most popular and best-selling, Li Xuan naturally ordered the set menu that included these dishes... No, he still ordered the most expensive set meal, since it was the boss's treat anyway.
Everyone was in a different mood during this lunch. These students from the competition class felt severely hit when they were next to Li Xuan.
Xu Lingchu stared at Li Xuan with stars in his eyes, "Xuan, you are so smart..."
For the first time, she had an intuitive experience of how good the brain is. This can explain the reason why Li Xuan was able to quickly go from the bottom of his grade to the second in his grade. Not everyone has such a brain. Her boyfriend is indeed the best in the school.
The smartest.
A good mind, instead of rebirth, explains the reason for his progress. Li Xuan also hoped that everyone would think so, so he did not explain anything.
Li Xuan passed his finger across her mouth, took a piece of rice from her lips, and then gave her an egg roll, "Eat more to nourish your brain."
When Xu Lingchu saw Li Xuan bringing food to her, she felt very happy and protested softly: "...I'm not stupid."
Li Xuan smiled and touched her head. With her by his side, the air was very sweet.
…
…
Before class in the afternoon, Li Xuan went to the mathematics office to find Zhao Dongming and bowed: "Teacher Zhao, thank you for your cultivation these days."
When Zhao Dongming saw Li Xuan, he felt very emotional. He quickly smiled and patted Li Xuan on the shoulder: "Classmate Li Xuan, come on, don't live up to your talent!"
Li Xuan nodded. There is no banquet in the world that lasts forever. He will remember the teacher's kindness to him.
…
…
Class was about to start, and when he returned to the competition class classroom, Li Xuan was sitting in the third row by the window, which was a great location.
Because the mathematics competition class was reorganized, a large number of new people were recruited. Because of the school's call, many people who did not want to participate in the competition came to join in the fun. The classroom of 60 people was full, and it could be described as an unprecedented event.
In addition to the boys, there are six new girls.
Li Xuan glanced at the classroom and unexpectedly saw Qiao Siling coming too.
Qiao Siling sat in the front row. She originally didn't want to get involved in the competition, but last week's competitive class exam was about high school mathematics. She did so well on the math test that coach Lin Xuerui came to find her:
"Are you Qiao Siling? In this competitive class exam, your math was ranked second in the first year of high school, only worse than Li Xuan. You also learned the knowledge in the second and third years of high school early? Why not come to the competitive class? You can consider studying in the competitive class."
Qiao Siling's mother heard about the competition class and asked her to participate.
So she came anyway.
Qiao Siling turned her head and saw Li Xuan looking at her and pursed her lips. To be honest, she was very curious in her heart and wanted to see how good Li Xuan was in mathematics.
This time, the competitive class policy has really taken off in the school. Those with good academic performance will almost always sign up for one class, and there are many masters in the competitive class.
The school recruits more than one coach, and each competition class is led by a coach. The coach of Class 1 of the Grade 1 Mathematics Competition is a graduate student from the School of Mathematics at Peking University, with the largest background.
Li Xuan heard the classmates around him talking about the new coach.
"I heard that the coach is a graduate student from Peking University."
"Beijing University?"
"I also heard that he is a CMO gold medal winner."
"Oh my god, this is like a god descending to earth."
"..."
Speaking of the new coach, respect appeared in the eyes of all the students unconsciously. Li Xuan thought the new coach was great, not to mention the other students. The new coach didn't seem to be short of money, and he probably came to teach high school math Olympiads just for fun.
Soon, the school bell rang.
Lin Xuerui walked into the classroom on time and didn't waste any time on the podium. She wrote her name on the blackboard, "Hello everyone, this is my name Lin Xuerui."
For a moment, all the students were afraid to speak.
Lin Xuerui looked at the students under the podium, smiled and said: "After everyone enters the competition class, the first goal must be very clear, which is to win prizes in the competition, recruit students and recommend students independently. I ask you to be more diligent than the students in the key class. No
With this realization, I suggest you withdraw from the competitive class immediately. When you are in your second year of high school and you don’t get the provincial third prize, don’t come to study for the competition. Concentrate on the college entrance examination and don’t waste time.”
The minimum requirement for the second year of high school is provincial three. Most of the students present felt a very distant feeling after hearing this.
Lin Xuerui said: "As someone who has experienced it, I have another suggestion, that is, everyone should take the time to go through high school knowledge in the first year of high school."
Yan Pengfei raised his hand and complained: "Coach, we are only in the first year of high school, there is no need to rush."
Lin Xuerui listened and shook her head:
"The knowledge in high school is actually very simple. It's just a superficial subject, and it's not even an introduction. I don't think anyone here can't understand it from the textbook, right? Open the catalog, just learn the concepts, and just look at the examples. You can complete one subject in a week. You can compete.
Ben, who thinks that his brain is not good?"
Yan Pengfei was stunned and did not dare to speak.
Lin Xuerui continued: "The difficulty of the college entrance examination is that the question types are complex and changeable. Only by answering a lot of questions can you train your problem-solving skills. Even if you read the textbook, you will not know how to do the college entrance examination paper, so I suggest you read the textbook first.
It’s about having a systematic grasp of high school knowledge.”
"Self-study is a very important skill. When you go to university and start working, you have to learn a lot of knowledge by yourself. There are no teachers to teach you. The knowledge you were exposed to at that time was much more complicated than the textbooks we have now."
"Although the competition class mainly studies mathematics, teachers will still come to teach other subjects. You must also do your homework and do not fall behind in other subjects."
When compared with other teachers, all the students felt that this new coach thought at the speed of light, spoke extremely fast, did not talk nonsense, and could not keep up if he did not listen carefully.
Lin Xuerui added:
"Many people here used to be students in the mathematics competition group. Should they know the radical axis theorem and the four major theorems of plane geometry? It doesn't matter if they don't. Don't feel pressured by the new students. I will systematically teach the square arithmetic and plane geometry in the future.
The simplest content of the competition is something left by people thousands of years ago. If you don’t learn it seriously, don’t doubt your own brain.”
"Because I prefer number theory, I will start with the content of elementary number theory."
"Let's do a simple question first. The students who can calculate it will raise their hands first."
In order to let these students feel the beauty of science first, Lin Xuerui decided not to take any difficult classes today, but mainly to popularize the knowledge of number theory so that the students can appreciate the charm of number theory.
On the blackboard, she wrote down a question: Find the last two digits of 3^83.
3 to the 83rd power?
Many students below looked at it and fell into a state of confusion. With such a large amount of calculation, even using a calculator could not calculate the last two digits.
The classroom was quiet, everyone was lowering their heads to calculate, picking up their calculators, or starting to count with their pens.
Lin Xuerui glanced at it and found that Li Xuan had raised his hand, and smiled, "Li Xuan, you can put your hand down first and wait for the other students."
When the other students saw it, they collapsed a little, "Nah... is this settled?"
"Human calculator, this is..."
"No, calculators aren't that fast either!"
"The Great God will not give people a way to survive..."
Qiao Siling was stunned, looked back at Li Xuan, and then frowned slightly as she looked at the question.
Liang Zhihui gritted his teeth and once again felt an inexplicable sense of oppression from Li Xuan. He quickly wrote and calculated, and he quickly figured out the answer and raised his hand.
In the following time, several students raised their hands one after another.
Li Xuan didn't feel anything. This question was really not difficult. It was an introductory question on number theory. By the second year of high school, or at the latest the third year of high school, he could be sure that all the students still here would do this kind of question.
A few minutes passed. Lin Xuerui saw that most of the students had failed to calculate. She had a general understanding of the level of this group of students. Of course, she was not disappointed. After all, she had not learned number theory since elementary school. It didn't matter if she didn't know it.
I can definitely teach it well, but I'm just worried that the students won't work hard.
She thought for a moment and pointed to Li Xuan, "Li Xuan, please tell me the answer."
Li Xuan stood up and said: "27."
Lin Xuerui nodded: "Yes, the last two digits of 3^83 are 27. How did you calculate it?"
Lin Xuerui turned around and quickly wrote on the blackboard:
3^0=1
3^1=3
3^2=9
3^3=27
3^4=81
3^5=243
3^6=729
3^7=2187
…
It can be seen from this.
The ones digit of 3^n power is a cycle of 1,3,9,7, and the cycle period is 4.
The tens digit of 3^n power is 0,0,0,2,8,4,2,8,6,8,4,4,4,2,6,0,2,6,8,6 cycle, cycle
To be continued...