Chapter 294

"You kid, you're going to tear down my platform as soon as you come back!"

Old Tang looked at Cheng Nuo, who was standing beside him and had obviously grown a lot, and couldn't help laughing and scolding.

Cheng Nuo smiled, "Teacher, I'm not doing this for the younger students, okay?"

Old Tang pushed to the side of the podium and left the stage to Cheng Nuo, and he motioned to Cheng Nuo, "Start your performance." ”

Under the gaze of more than 30 juniors and sisters, Cheng Nuo took out a piece of chalk and spoke loudly.

"There is no problem with the proof steps that Mr. Tang told you about this question just now. So I didn't come up to find fault. ”

"It's just that, as you must have seen, the process of proving this question is too cumbersome. ”

Cheng Nuo circled the entire blackboard in a large circle. Then write down a proposition in the corner.

[As long as the initial six numbers are not even, odd, odd, even, odd, odd, and not all are even, then all numbers must be equal to zero through a finite number of operations.] 】

Cheng Nuo's fingers tapped heavily on the blackboard.

It can be clearly seen that the formula of this blackboard, the classification discussion, is all to prove this conjecture. If you're okay in your regular training and have plenty of time, you'll have plenty of time to take your steps slowly. However, in the competition, time is a race against seconds, so such a complex problem-solving process is not suitable. ”

"Senior, do you mean that you have a simpler proof process?" raised his hand to ask the short boy sitting in the first row, Chen Gong.

Chen Gong was sitting straight in his seat at this time, looking up at Cheng Nuo, who was extremely confident and eloquent on the podium, with a faint disbelief in his eyes.

Facing this junior's question, Cheng Nuo just smiled and nodded slightly, "That's right, when I listened to Teacher Tang talk about this topic just now, I did think of a simpler way to prove it. ”

Chen Gong raised his hand again, "Senior, the problem-solving method you use won't be the knowledge you only learned in college, right?"

Cheng Nuo shook his head, "Not really." To solve a problem of this difficulty, the knowledge learned in high school is sufficient. ”

Cheng Nuo turned sideways, erased half of the blackboard, and wrote three big characters on it.

Induction!

Induction, a very basic method of mathematical proof in high school, is usually used to prove that a given proposition is true within a range of natural numbers in whole (or partially). It is divided into the first mathematical induction method, the second mathematical induction method, the backward induction method, and the spiral induction method.

Seeing these three words on the blackboard, Chen Gong's eyes lit up, and he seemed to understand something, but the thoughts in his mind were still blurry.

As for the rest of the room, they still had confused expressions. Isn't it a discussion of parity, how can it be brought to the inductive method again?

Cheng Nuo wrote while talking about his thoughts.

“...... The steps in the previous section remain unchanged and we get the special value of 2. Later, we begin to prove this proposition by induction. The spiral induction method in the induction method is selected. ”

"Summarizing n, when n = 1 is obvious...... Next, let the given numbers a1 ≤ a2≦...... ≤am, and make Si=a1+a2+......+ai. ”

“...... In summary, n satisfying the condition is 2 and all positive odd numbers. ”

Certification.

The answer given is exactly the same as the standard answer.

What's more, what's even more terrifying is that Cheng Nuo's proof step only uses half a blackboard and more than a dozen lines of formulas. It's a world away from the previous two-blackboard proof formula.

It's scary, it's scary!

Bang Bang Bang!

Old Tang, who was standing on the side of the podium, raised his hands, applauded gently, and looked at Cheng Nuo on the side with approval and satisfaction.

Although he was demolished by Cheng Nuo today, Old Tang was not angry at all.

No matter how awesome Cheng Nuo is, he is still his own student! Being able to get such a student out of his hands is enough for him to brag about for a lifetime.

Bang Bang Bang!

The other students in the classroom also applauded in unison, and some of them were indeed impressed by Cheng Nuo's unique problem-solving ideas, such as Chen Gong. And some of them are just pure unconsciousness.

Suddenly, the sound of popping in the entire classroom was endless.

............

In the corridor, Cheng Nuo was catching up with Comrade Tang according to the railing. I saw a boy who was not tall, and walked in the direction of Cheng Nuo with some hesitation.

Cheng Nuo knew him, it was Chen Gong, who was sitting in the first row during the competition training just now.

I saw that classmate Chen Gong hesitantly walked up to Cheng Nuo, raised his head, a little embarrassed, and vomited for a long time before he said with a shy face, "Senior, I can add your > Cheng Nuo: ???

I...... I'm rubbing!

In an instant, Cheng Nuo felt a cool breath rise from the chrysanthemum down the tail vertebrae to his brain.

A sentence of MMP is enough to express Cheng Nuo's current mood.

Why? Why are the people who want to be WeChat all beautiful students, and they have become shy students?

Cheng Nuo subconsciously leaned over to Old Tang, "You...... What do you want to do?"

Chen Gong's face turned red, and he plucked up the courage of his whole body and said, "Senior, I want to be your person!"

"Uh, no, wrong, wrong, it's to be like you. ”

False alarm...... A false alarm!

Just now, Cheng Nuo was so frightened that he almost jumped directly from the fifth floor. It's so exciting.

Chen Gong explained the reason for asking Cheng Nuo's WeChat, "Senior, I think if you have any questions about mathematics, I can ask you at any time." ”

"It's okay, just ask, whatever you want. You are my own brother, and I will definitely teach you everything. "It doesn't matter what the question is, as long as it's not the person who becomes me, it's okay.

got Cheng Nuo's WeChat account, and Chen Gong left happily.

Next, Cheng Nuo and Lao Tang walked around the campus for a while. Originally, Cheng Nuo wanted to invite Lao Tang to have dinner together, but Lao Tang still had a few nights of self-study to stare, so he could only wait another day.

"There will be your lecture in school the day after tomorrow, so when you go back, you must prepare well and give a lesson to the group of little guys in the third year of high school. Strive to let our No. 2 Middle School win the top spot in the college entrance examination for a second time. ”

Cheng Nuo smiled bitterly and nodded yes. Won the top spot in the college entrance examination for a second time, and it seems that no school has ever done this thing in history.

Saying goodbye to Old Tang, Cheng Nuo found a small restaurant to make do with dinner, and then took a taxi home.

As soon as he returned to the bedroom, Cheng Nuo's mobile phone prompted him to receive a new message. I thought it was Mu Leng who sent me a test question similar to taking medicine, but I didn't expect to open WeChat and see that it was not Mu Leng's beautiful girlfriend who sent the message, but Chen Gong, the shy junior I just met today.

Chen Gong: "Huh, is the senior here?"

Chen Gong: "Can you help me look at this question?" ”

Attached is a photo taken with a mobile phone.

【Let f(x)=5x+2=f1(x), fn+1(x)=f[fn(x)].Verification: For any positive integer n, there is a positive integer m, so that 2011|fn(m)]