I Kidnapped An Alien Civilization

2021-07-07

Chapter 146 Proof

“Li Mo, you are a biology student, why are you reading group theory?”

“Li Mo, what are the mathematical symbols in this book?”

“Li Mo, you are very awesome, you can understand such a complex formula.”

… ………

In the library, Zhang Yazi approached Li Mo like a dog-skin plaster. Li Mo disliked her for being noisy and asked her to leave several times.

“Is the library opened by your family?” Zhang Yazi, who was like a flower and jade, pinched his waist with both hands, causing envious glances from the boys around him.

Li Mo had no choice but to shook the head, he had no experience with such a girl.

He decided to ignore Zhang Yazi’s words.

“Li Mo, the cytology class is about to start, won’t you go to class?”

“Li Mo, are you sure you won’t go to class, but the teacher will call you.”

In the end, Li Mo showed a triumphant smile as he watched Zhang Yazi helplessly leave with his schoolbag on his back.

Even under Zhang Yazi’s constant “harassment”, Li Mo still wrote the formula for perfect numbers: if 2^p-1 is a prime number, then (2^p-1)X2^( p-1) is a perfect number. For example, p=2, 2^p-1=3 is a prime number, (2^p-1)X2^(p-1)=3X2=6, it is a perfect number.

According to this formula, all perfect numbers can be generated.

However, according to this formula, it cannot be concluded that perfect numbers cannot exist in odd numbers, and further constraints need to be set.

For a whole day, Li Mo calculated the first constraint. If there is an odd perfection, then this odd number cannot be divisible by 105. This excludes factors and multiples of 105.

“Why are mathematical problems in numbers always difficult to solve, because they can be applied to too few high-level theorems and axioms.” Li Mo couldn’t help but look at the head, no wonder Professor Wu suggested that he change topic.

After dinner, Li Mo ran laps on the sports field with Xia Qing as usual, and he has now developed the habit of thinking while running. “It’s almost impossible to prove that odd numbers are perfect by the method of constraints.”

In running, he rejected the results of his day’s hard work. When it comes to solving math problems, a wrong idea is the most terrifying, and it can cost you energy and get nothing. The experienced Li Mo predicted the error of this method in advance.

At night, Li Mo turned on the lamp and thought hard about new ideas. “A virtual number? I can come up with a virtual odd number and pretend that this odd number has the characteristics of a perfect number.”

He thought of a new idea, “virtual number”.

A “perfect odd number” should have all the properties of a “virtual number”, but also with special conditions.

And if it can be proved that “virtual” does not meet any of the constraints of “perfect odd”, then “perfect odd” exists impossible.

Simply put, since a “perfect odd number” is not divisible by 105, then if all “virtual” numbers are divisible by 105, a “perfect odd number” does not exist.

Li Mo thought, the job now becomes to prove the existence of this “virtual number”.

The idea becomes clear all at once. First of all, it is necessary to enumerate the characteristics of perfect numbers: Properties of perfect numbers 1: They can all be written as the sum of consecutive natural numbers: 6=1+2+3; 28=1+ 2+3+4+5+6+7; 496=1+2+3+30+31

Property 2: The sum of the reciprocals of all their factors is 2: 1/1+1/2 +1/3+1/6=2; 1/1+1/2+1/4+1/7+1/14+1/28=2

Property 3: All perfect numbers They all end in 6 or 8.

In the early morning, Li Mo felt that he had reached the edge of the answer. He took out his mobile phone and sent a WeChat message to Xia Qing: “Do not disturb during retreat.”

Then he took out a bottle of energy coffee from the “warehouse” and knocked it down without the slightest hesitation.

Inspiration came inadvertently, Li Mo wrote:

Constraints: 1. It has at least 6 different prime divisors;

2 , it must have the (4X+1) power of P times the 2a1 power of Q1 times the 2a2 power of Q2 times. . . . Multiply by Qn to the power of 2an (“1” of Q1 and 2a1 is the subscript), where P must be a prime number in the form of 4K+1, and Q can be any odd prime number;

3. If the above If all other as except a1 are equal to 1, then a1 cannot be equal to 2; if all other as except a1 and a2 are equal to 1, then a1 and a2 cannot both be equal to 2;

4. If all Q’s If the exponents are all incremented by 1, the resulting exponent cannot have 9, 15, 21 or 33 as a common divisor;

5. All a cannot be equal to 2;

6. All The exponent 4X+1 of P is equal to 5, then all a cannot be equal to 1 or 2.

7. If it is not divisible by 3, it must have at least 9 different prime divisors; if it is not divisible by 21, it must have at least 11 different prime divisors; if it cannot be divisible by 21 If it is divisible by 15, it has at least 14 different prime divisors; if it is not divisible by 105, it has at least 27 different prime divisors; this would require that the odd perfect number be at least greater than 10 to the 44th power.

So an+1-an has the same sign as an-an-1. According to mathematical induction, ?n∈N+, an+1-an has the same sign as a2-a1. Therefore, the necessary and sufficient conditions for an+1>an for all n∈N+ are 03.

It can be seen that there is no odd number that satisfies all constraints.

There is no such thing as a perfect number.

The odd perfect conjecture proves the ratio.

Writing the last mathematical symbol, Li Mo closed his eyes, he felt the bud of wisdom send out another branch in the back of his mind.

“It’s no wonder that so many well-known mathematicians in history have not broken this seemingly simple conjecture. It turns out that the constraints themselves are traps, and the world of numbers is amazing.”

The next step is to organize the papers into drafts. This time, Li Mo decided to write one manuscript each in Chinese and English.

“It’s the fifth day, Boss won’t faint in the room, right?” Xia Qing in the living room thought while eating the cone, “Forget it, leave him alone, after all, Boss is not Ordinary people.”

After eating the cone, she was about to pick up the oranges on the coffee table and looked at her snow-white fingers. “Oops, I need to lose weight. It’s all because of that damn Li Mo, doing some kind of retreat, so I can only stay here all day.”

She hesitated, and finally gave up the tempting Orange, “An orange has 50 calories and needs to run 800 meters.” She looked all around, and there was no fitness equipment in the living room. The final decision was to do aerobics, and she turned on the TV and turned the volume down to minimum. Jump to the rhythm on TV.

This is what Li Mo saw when he opened the door. The tall Xia Qing, who was wearing tight pants, followed the TV, posing in various poses.

“Boss, are you out?” Xia Qing said while jumping, “Ah! Close your eyes!” She suddenly realized that her clothes were a little cool, and immediately fled back to the room.

This Xia Qing looks like a child. Li Mo shook the head.

(End of this chapter)