Become a master from now on

Chapter 104 Goldbach and Euler

When the examinees did not make it to the final round of the national finals, the pressure was actually not that great.

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

This is an exam of the highest level of mathematics in China. Everyone wants to stand out in this kind of competition, and after deducting those candidates who have been eliminated, one can imagine how much pressure is superimposed on them.

Especially for provinces and cities that have always been victorious generals in the past, this kind of pressure is far more terrifying than others.

Hubei, BJ, Zhejiang, Guangdong and other places.

The one whose mentality collapsed just now was a senior high school candidate from Guangdong. There was no way he could solve any of the three questions for more than two hours.

There must be a psychologist, and there must be more than one. These candidates are the future pillars of the motherland, and we cannot let them have problems easily.

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

And just 3 minutes later, a candidate fell down again.

"No, this candidate is foaming at the mouth, doctor, doctor!"

This time, it was not a psychological pressure, but a physical problem.

On the field of the national finals, there are frequent situations, especially in recent years, the psychological and physical qualities of the candidates are getting weaker and weaker, and they even run away from home at every turn or are directly depressed, which is more serious They all open the windows directly to take a leap when they are in class.

So much so that even teachers are under more and more pressure these days. You can’t hit or scold. The masses will flesh you out and put things on the bright side, and many teachers have suffered from troubles in life because of this.

In the past, beating students with a ruler basically did not happen in recent years.

But in Fang Chao's view, a certain amount of punishment may not be a good thing for students, too much smooth sailing will make people's mentality too fragile.

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

This third question is a bit interesting.

The title is sweet and purple: Let the integer n≥3, there are k prime numbers not exceeding n, let A be a subset of the set {2, 3,...,n}, the number of elements in A is less than k, and any One number is not a multiple of another number,

Proof: There is a k-element subset B of the set {2, 3, ..., n}, such that any number in B is not a multiple of another number, and B contains A.

This question is about prime numbers.

Interesting.

Prime numbers are also called prime numbers.

According to the Fundamental Theorem of Arithmetic, every integer greater than 1 is either itself a prime number, or can be written as a product of a series of prime numbers, and if the order of these prime numbers in the product is not considered, then the written form is unique.The smallest prime number is 2.

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

So far, people have found that the largest prime number is 2233 million digits long. If it were printed in ordinary font size, the length would be more than 65 kilometers.

This also represents the infinite possibility of prime numbers.

He can cause a lot of trouble in mathematics, but he also makes mathematicians happy.

From this, countless conjectures were born.

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

又或者说是，斐波那契数列内是否存在无穷多的素数？是否有无穷多个的梅森素数？在n2与（n+1）2之间是否每隔n就有一个素数？是否存在无穷个形式如X2+1素数？

And the most famous Goldbach conjecture.

About 270 years ago, Goldbach wrote a letter to Euler. Everyone knows that technology was not developed enough in the past. At that time, you can’t expect to have QQ and WeChat, right?Of course, there wasn't even a phone back then.

It is under such circumstances that if you want to make friends, you have to write letters. Everyone is very strange and mysterious. If the boyfriend and girlfriend in the earliest days have a crush, they will first have a letter exchange. The content in my heart was still very reserved at that time, and it was not explicit at all. After a month or so of correspondence, everyone would propose to meet each other. We have nothing in common.

As a German mathematician, Goldbach is a smart man, 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 be recognized by others, then you must first be at least as good as me in mathematics, right?Otherwise, wouldn't it be embarrassing if everyone couldn't talk together in the future?

Mathematicians play letters with others?Are you in a hurry?
Besides, there were really too few mathematicians at that time, so few.

Ever since, in a special environment, Goldbach and Euler became pen pals, and they went back and forth for more than [-] years.

When eating one day, Goldbach thought of a problem, but he was so dizzy thinking about this problem that he couldn't figure it out, so he thought of his good friend Euler.

Then he wrote in the letter, "Brother Euler, I have encountered a problem now, can you help me solve it?

随便取某一个奇数，比如77，可以把它写成三个素数之和：77=53+17+7；

Take another odd number, such as 461, 461=449+7+5, which is also the sum of three prime numbers. 461 can also be written as 257+199+5, 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 experiment that has been done has yielded the above results, it is impossible to test all odd numbers. What is needed is a general proof, not an individual test, right?Brother Ola, you are so smart, you can definitely help me figure it out, right? "

As we have said before, mathematicians are all proud and arrogant, and Goldbach has already flattered them all, and all of them are on the key points. The most important thing for a mathematician is to be able to get Another mathematician's affirmation, as his good friend, Euler must affirm Goldbach's strength, even his little brother asks himself, how can he not let him down, right?
So he replied, "I agree with your proposition!"

(End of this chapter)