I kidnapped an alien civilization

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 so good, you can understand such a complicated formula.

…………

In the library, Zhang Yazi approached Li Mo like a dog's skin plaster. Li Mo despised her noisy and asked her to leave several times.

Your family runs the library, right? Zhang Yazi, who was as beautiful as a flower, pinched her waist with both hands, causing envious eyes from the boys around her.

Li Mo had no choice but to shake his head helplessly. He had no experience with such girls.

He decided to adopt the strategy of ignoring it, turning a deaf ear to Zhang Yazi's words.

Li Mo, the cytology class is about to start, why don't you go to class?

Li Mo, if you are sure not to go to class, the teacher will call the roll.

In the end, Li Mo looked at the back of Zhang Yazi leaving helplessly with his schoolbag on his back, and smiled triumphantly.

Even under the constant harassment by Zhang Yazi, Li Mo still wrote out the formula of the perfect number: 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, and (2^p-1)X2^(p-1)=3X2=6 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 condition, if there is an odd perfect number, then this odd number cannot be divisible by 105. This excludes factors and multiples of 105.

Why are mathematical problems in numbers always so difficult to solve? Because there are too few advanced theorems and axioms that can be applied to them. Li Mo shook his head involuntarily. No wonder Professor Wu suggested that he change the topic.

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

On the run, he vetoes the fruits of his day's hard work. For mathematical problem solving, a wrong problem-solving idea is the most terrifying, it may exhaust your energy and achieve nothing. The experienced Li Mo predicted the error of this method in advance.

At night, Li Mo turned on the desk lamp, thinking hard about new ideas. Virtual number? I can propose 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.

Perfect odd number should have all the characteristics of virtual number, but also has its own special conditions.

And if it can be proved that virtual does not meet any of the constraints of perfect odd number, then perfect odd number cannot exist.

In simple terms, since perfect odd numbers are not divisible by 105, then if all virtual numbers are divisible by 105, perfect odd numbers do not exist.

Li Mo thought, the job now is to prove whether this virtual number exists.

The idea suddenly becomes clear. First, we need to enumerate the characteristics of perfect numbers: Property 1 of perfect numbers: They can all be written as the sum of continuous natural numbers: 6=1+2+3; 28=1+2+3+4+5 +6+7; 496=1+2+3+30+31

Nature 2: The reciprocal sum 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 end in 6, 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 Xia Qing a WeChat message: Do not disturb during retreat.

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

Inspiration came inadvertently, and Li Mo frantically wrote:

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

2. It must have the (4X+1) power of P multiplied by the 2a1 power of Q1 multiplied by the 2a2 power of Q2. . . . Multiplied by Qn to the power of 2an (1 in 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 formula except a1 is equal to 1, then a1 cannot be equal to 2; if other a except a1 and a2 are equal to 1, then a1 and a2 cannot both be equal to 2;

4. If the exponents of all Qs are incremented by 1, the resulting exponents cannot have 9, 15, 21 or 33 as common divisors;

5. All a cannot be equal to 2;

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

Therefore 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 condition of an+1\u003ean for all n∈N+ is 0\u003ca1\u003c1 or a1\u003e3.

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

So there is no such thing as an odd number meeting the characteristics of a perfect number.

Proof of odd perfect conjecture.

After writing the last mathematical symbol, Li Mo closed his eyes, and he felt the sprout of wisdom sprouting another branch deep in his mind.

It's no wonder that so many well-known mathematicians in history have not broken through this seemingly simple conjecture. It turns out that the constraint itself is a trap, and the world of numbers is so wonderful.

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

It's already 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 an ordinary person.

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 the fault of that damned Li Mo, what kind of retreat, I can only stay here all day.

She hesitated for a while, and finally gave up the attractive orange, One orange has 50 calories, and you need to run 800 meters. She looked 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 was wearing leggings, following the TV, posing in various poses.

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

This Xia Qing, why is she like a child. Li Mo shook his head.