I kidnapped an alien civilization

Keep going! Li Mo clicked on the release of new tasks.

New mission released! The general on horseback appeared again on the screen.

Task: A good student who can't write a paper is not a good student, so let's publish a paper. juvenile!

Task description: Please publish an academic paper in any academic journal or newspaper.

Task reward: 3000 points, draw once.

Task time limit: ten days

Writing a math paper? Li Mo looked at the collection of math problems on the desk, wondering if he could write a paper by solving a math problem that no one had solved.

But where is it published? Li Mo turned on the phone and dialed, and asked if he didn't understand. It was Li Mo's awareness of being a scumbag in the past.

"Mr. Zhang, hello, I'm your student Li Mo. I want to ask a question. I want to write a mathematics paper. I don't know where to publish it."

Li Mo called his math teacher. He once heard other teachers say that Mr. Zhang has a high level of mathematics, but he was assigned to teach in their school because he was unsophisticated.

"Li Mo, student, hello, what do you want to publish...?" Mr. Zhang thought he heard it wrong. In his impression, Li Mo's grades were mediocre, so how could he publish a paper.

"Publishing mathematics papers, I want to ask the teacher, where is the best place to publish mathematics papers." Li Mo repeated.

"Mathematics papers, generally speaking, "Mathematics Monthly" has more readers and stronger credibility. But it is very difficult to submit. I think it is better for you to publish on "Mathematics for Middle School Students", which has more popular science. The difficulty is also lower." Teacher Zhang explained in detail.

"By the way, what kind of mathematics paper did you write?"

"Oh, I haven't written it yet, and I haven't submitted a manuscript, so ask the teacher." Li Mo replied honestly.

"Didn't write?? Li Mo! Are you playing truth or dare? The teacher's time is also very precious!"

Beep. Beep. Beep.

Li Mo was a little dazed looking at the phone that Teacher Zhang hung up on directly, he didn't know how he made Teacher Zhang angry.

It's easy to know where to publish. It is the most difficult question for Xueba, and the most difficult paper to publish. The goal is determined! Mathematical Monthly.

Li Mo took out the collection of world problems. This book is a collection of all the problems in the world, including solved ones and unsolved ones. This book was bought by Li Mo's mother when he was in elementary school. It was shelved.

Opening the title page, there is a passage from Einstein in the preface - one reason why mathematics is more respected than all other sciences is because his propositions are absolutely reliable and indisputable, while other sciences are often in the process of being newly discovered. The danger of overturning the facts. ...Another reason why mathematics has a high reputation is that mathematics enables theoremization of natural science and gives natural science a certain degree of reliability.

The fundamental reason why mathematics can become the foundation of other subjects is that the results of mathematics are absolutely reliable and indisputable. No wonder the learning machine system requires me to raise my math level to level 6 first.

The catalog lists unsolved problems in the history of mathematics.

1. NP complete problem

Example: On a Saturday night, you attended a big party. Embarrassed, you wonder if there is anyone in the hall you already know. The host of the party proposes to you that you must know the lady Rose in the corner near the dessert plate. It doesn't take a second for you to glance there and see that the host of the party is correct. However, without such a hint, you'd have to look around the hall, checking everyone one by one, to see if there was anyone you knew.

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Generating a solution to a problem usually takes much more time than verifying a given solution. This is an example of this general phenomenon. Similarly, if someone tells you that the number 13717421 can be written as the product of two smaller numbers, you might not know whether to believe him, but if he tells you that it can be factored as 3607 times 3803, then you This can easily be verified with a pocket calculator.

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It was found that all complete polynomial non-deterministic problems can be transformed into a class of logical operation problems called satisfiability problems. Since all possible answers to such questions can be calculated in polynomial time, people wonder whether there is a deterministic algorithm for this kind of problem, which can directly calculate or search for the correct answer in polynomial time? This is the famous NP=P? conjecture. Regardless of how dexterously we write programs, deciding whether an answer can be quickly verified using internal knowledge, or takes a lot of time to solve without such hints, is regarded as one of the most prominent problems in logic and computer science. It was stated by Steven Cocker in 1971.

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programming? logic operation? computer Science? ?

Li Mo couldn't understand, most of the mathematical knowledge used here he hadn't mastered yet.

Forget it, let's look at the next question.

BSD conjecture

2. Poincaré conjectured that any closed three-dimensional space, as long as all the closed curves in it can be shrunk to a point, this space must be a three-dimensional sphere

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The title of this question is incomprehensible. . next one.

3. The Hodge conjecture asserts that for a particularly perfect type of space called projective algebraic varieties, components called Hodge closures are actually (rational linear) combinations of geometric components called algebraic closures.

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He knows all the Chinese characters in the question, why can't he understand them together?

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I can’t understand this question, I can’t understand this one, what does the title of this question mean? ?

Li Mo's face turned ugly, remembering that he was only at the second grade in mathematics, it was really too difficult to use his high school knowledge to try to solve an unsolved problem.

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Give up those questions whose names you don't understand, and only choose those within the scope of high school mathematics. Li Mo accelerated the speed of "turning the page".

Finally, he found a problem that fully fit the scope of high school knowledge.

Collats conjecture, also known as 3n+1 conjecture, Kakutani conjecture, Hasse conjecture, Ulam conjecture or Syracuse conjecture.

It means that for each positive integer, if it is an odd number, multiply it by 3 and add 1, if it is an even number, divide it by 2, and so on, and finally get 1.

The Collats conjecture can also be called the "odd-even normalization conjecture".

In 1930, Koraz, a student at the University of Hamburg in Germany, studied this conjecture, hence the name.

"positive integer", "even", odd. Awesome, simple and totally understandable.

If you want a positive integer, let this number be x and if the next number is odd, then multiply it by three and add one, that is 3x+1, if x is even, then divide it by two, that is x÷2 , then this number will eventually become 1 through 4 and 2.

If the imagined number is 3, then it is 3×3+1=10, 10÷2=5, 5×3+1=16, 16÷2=8, 8÷2=4, 4÷2=2, 2 ÷2=1.

Li Mo checked the content of the question with a pen, and it was completely correct, but how to prove it?

Induction. . no.

Use the theorem to prove directly. . . no.

swish. . swish. . swish. .

A paper. . two sheets of paper. . Three sheets of paper. .

One hour. . two hours. . three hours. .

Pull out a bottle of energy coffee, now is not the time to save.

Its daybreak. . it's dark. .

Or not! Or not!

He was a little discouraged, closed his eyes and meditated, thinking slowly.

It seems that the conventional problem-solving ideas are completely incomprehensible.

Isn't there still a drop of inspirational water?

There is only one drop in the small bottle, and it drips into the mouth, which is a little sweet. .

It doesn't seem to work. . It can't be a fake.

"Wait...I thought of it..." A flash of light suddenly flashed in my brain.

n is an even number, n/2 is an even number, ..., always divide 2 to 1; n is an even number, n/2 is an even number, until n is divided by 2 to the X power, it is an odd number. We represent n divided by 2 to the X power as n, which can be equivalent to n being an odd number. (When it is an even number, the number must be decreasing)

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n is an odd number, n×2+n×1+1 2n+n+1, this must be an even number, (2n+n+1)/2 n+(n+1)/2, there are two situations here, as If it is an even number, it is an odd number; if it is an even number, cycle ① (the number keeps decreasing when it is an even number), until n+(n+1)/2 is an odd number.

Because: n is an odd number, there is and only (n+1)/2 is an even number 1 n+(n+1)/2 can be an odd number.

n is an odd number, n+(n+1)/2 is an odd number, continue below:

n+(n+1)/2 is an odd number, ×2+×1+1 2n+n+1+n+(n+1)/2+1, 2n+1+(n+1)/4 is an even number, divide Take 2 2+×1+1 2n+n+1+n+(n+1)/2+1

Continue the two cases, if it is an even number, it is an odd number, and if it is an even number, cycle ① and ②, (Anyway, the number is decreasing when the number is even)

, until 2n+1+(n+1)/4 is an odd number. Transform to n+(n+1)+(n+1)/4

Because: n is an odd number, n+1 is an even number, and only (n+1)/4 is an even number, and n+n+1+(n+1)/4 can be an odd number.

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n+2(n+1)+(n+1)/4+(n+1)/8 is an odd number, ×2+×1+1

2n+4(n+1)+(n+1)/2+(n+1)/4+n+2(n+1)+(n+1)/4+(n+1)/8+ 1

10n+8+(n+1)/8 is an even number, divided by 2 5n+4+(n+1)/16

n+4(n+1)+(n+1)/16

Infinite loop until (n+1)/2 gets x power=1

So far the proof is complete.

For each positive integer, if it is an odd number, multiply it by 3 and add 1, if it is an even number, divide it by 2, and so on, and finally get 1. This conjecture is completely correct.

Li Mo put down the pen in his hand and closed his eyes. He felt the storm of wisdom rolling in his head, and a power deep in his soul was slowly awakening.

Looking at the alarm clock, he has not closed his eyes for 74 hours. His eyes darkened, he fainted on the bed, his dying consciousness "I still have papers to write..."