The pressure on candidates was not really huge when they did not enter the last game of the national finals.

They are selected by the school, then the provincial preliminary and preliminary competitions, and then they can participate in the CMO event... After experiencing the difficulty of the first half assessment, the psychological pressure on them in the second half has become even greater.

This is the highest level of mathematics in China. Everyone wants to stand out in such a competition. And if you deduct the candidates who have been eliminated, you can imagine how much pressure you are superimposed on them.

Especially for provinces and cities that have been victorious generals in the past, such pressure is much more terrifying than others.

Hubei, Beijing, Zhejiang, Guangdong and other places.

The one who broke his mind just now was a Guangdong high school senior candidate. There was no way, and he couldn't solve any three questions for more than two hours. This made his mood break his balance and he collapsed.

There must be something that psychologists need, and there is more than one. These candidates are the pillars of the motherland's future, so they can't easily have problems.

Soon, a professional psychological counselor went to teach the candidates just now.

And just three minutes later, a candidate fell down again.

"No, this candidate foamed at the mouth, doctor, doctor!"

This time, it’s not psychological pressure, but physical problems.

On the national finals, situations occur frequently, especially in recent years, candidates' psychological and physical fitness have become increasingly weak, and they even run away from home at any time or become directly depressed. In serious cases, they can directly open the window during class to make a leap.

So much so that even teachers are under increasing pressure these days. You can’t beat them, and you can’t scold them. If you are too much, you will corporal punishment for students. Moreover, the Internet is transparent now. If you really want to do something, the people who don’t know the truth will be tyrannical and put things on the surface, and many teachers have also suffered from life difficulties.

In the past, the fact that the students were hit with a ruler had basically not happened in recent years.

However, in Fang Chao's opinion, certain punishment may not be a good thing for students. Too smooth sailing will make people have too fragile mentality.

Fang Chao ignored these people and started to do the third question on his own.

This third question is a bit interesting.

The title is Jianzi: Assume that the integer n≥3, there are k prime numbers that do not exceed n, and assuming a is a subset of the set {2,3,...,n}, the number of elements of a is less than k, and any number in a is not a multiple of another number,

Proof: There is a k element subset b of the set {2,3,...,n}, so that any number in b is not a multiple of the other number, and b contains a.

This question tests prime numbers.

Very interesting.

Prime numbers are also called prime numbers.

According to the basic theorem of arithmetic, each integer larger than 1 is either a prime number itself or can be written as the product of a series of prime numbers. And if the order of these prime numbers in the product is not taken into account, the written form is unique. The smallest prime number is 2.

So far, people have not found a formula to find all prime numbers.

So far, people have found that the largest prime number is as long as 22.33 million digits, and if it is printed with a normal font size, it will be more than 65 kilometers long.

This also represents the infinite possibilities of prime numbers.

He was able to give great trouble in mathematics, but it also made mathematicians enjoy it.

This has resulted in countless conjectures.

For example, twin prime numbers are prime pairs with a difference of 2, such as 11 and 13. Do there are infinitely many twin prime numbers? This is also an extremely famous conjecture, twin prime numbers conjecture.

Or, is there an infinite number of prime numbers in the Fibonacci sequence? Are there infinite number of Mason prime numbers? Is there a prime number every n between n2 and (n1)2? Are there infinite forms such as x21 prime numbers?

And the most famous Goldbach conjecture.

About two hundred and seventy years ago, Goldbach wrote a letter to Euler. Everyone knows that in the past, technology was not yet developed enough, and you could not expect QQ and WeChat at that time, right? Of course, even the phone was not available at that time.

It is in that situation that if you want to make friends, you have to write a letter. Everyone is unfamiliar and mysterious. At the earliest, if a boyfriend and girlfriend admire him, they will first have a letter exchange. The content in their hearts was still very subtle and not explicit at all. About a month after the letter exchange, everyone will ask to meet. If we can chat, we will formally date after we can't chat. If we can't chat, we will stop the letter. We have no common topic.

As a German mathematician, Goldbach is a smart person, and it is not easy to become a pen pal with him.

Mathematicians are arrogant and lonely, but they are also extremely proud. If you want to get recognition from others, then you must first be at least comparable to me in terms of math level, right? Otherwise, it would be awkward if you can't talk to each other in the future?

Mathematicians are playing with letters with others? Are they indolent?

Besides, there were really too few mathematicians at that time, very few.

So, in a special environment, Goldbach and Euler became pen pals, and this time they lasted for more than thirty years.

One day during dinner, Goldbach thought of a question, but as for this question, he was so dizzy that he didn't think of it, so he thought of his good friend Euler.

Then he wrote in the letter, "Brother Ola, I am facing a difficult problem now. Can you help me solve it?

Take an odd number, such as 77, and you can write it as the sum of three prime numbers: 77=53177;

Take an odd number, such as 461, 461=44975, which is also the sum of three prime numbers. 461 can also be written as 2571995, which is still the sum of three prime numbers. In this way, I found that any odd number greater than 9 is the sum of three prime numbers.

But how to prove this? Although every test I have done has obtained the above results, it is impossible to use all odd numbers to test. What is needed is general proof, not individual proof, right? Brother Ola, you are so smart, you can definitely help me with it, right?"

As we have said before, mathematicians are all proud and arrogant. Besides, Goldbach has already flattered them all, and they are all on key points. The most important thing for a mathematician is to be recognized by another mathematician. As his good friend, Euler must be affirming Goldbach's strength. Even his little brother demands himself, so he can't let him down, right?

So he replied, "I agree with your proposition!"
Chapter completed!