Keep up the good work! Li Mo clicked on the new task release.

New mission released! The mounted general appears on the screen again.

Task: A top student who can’t write a paper is not a good top student. Publish a paper. Boy!

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

Task reward: 2000 points, one draw.

Mission time limit: ten days

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

But where to publish it? Li Mo turned on his mobile phone and dialed. He didn't understand and asked about Li Mo's former self-consciousness as a bad student.

"Hello, Teacher Zhang, I am your student Li Mo. I would like to ask, I want to write a mathematics paper, but I don't know where to publish it."

Li Mo called his mathematics teacher. He had heard from other teachers that Teacher Zhang was very good at mathematics, but he was assigned to teach in their school because he was not very understanding of the world.

"Li... hello, classmate Li Mo, what do you want to publish...?" Teacher Zhang thought he had heard wrong. In his impression, Li Mo had mediocre grades, so how could he possibly publish a paper.

"I would like to ask the teacher where it is better to publish a mathematics paper." Li Mo repeated it again.

"Mathematical papers... Generally speaking, "Mathematics Monthly" has more readers and has stronger credibility. But it is very difficult to submit an article. I think it is better for you to publish it in "Middle School Student Mathematics", which has more popular science topics.

Some, the difficulty of submission is also lower." Teacher Zhang explained in detail.

"By the way, what is the mathematics paper you wrote about?"

"Oh...I haven't written it yet. I haven't submitted any manuscripts, so I'll ask the teacher." Li Mo answered honestly.

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

Beep...beep...beep...

Li Mo was a little confused when he saw Teacher Zhang hanging up the phone. He didn't know how he made Teacher Zhang angry.

It will be easier if you know where to publish. It is the most difficult problem for top students and the most difficult paper to publish. The goal is set! "Mathematics Monthly".

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

He was put on the shelf.

Opening the title page, there is a passage from Einstein in the preface - One reason why mathematics is respected above all other sciences is because its propositions are absolutely reliable and indisputable, while other sciences are constantly being discovered.

The danger of overturning the facts... Another reason why mathematics has a high reputation is that mathematics enables natural science to realize theorems 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 upgrade my mathematics 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 grand party. Feeling awkward, you wondered if there was anyone you already knew in the hall. The host of the party suggested to you that you must know that person.

Lady Rose is in the corner near the dessert plate. It doesn't take you a second to glance there and see that the host of the party is correct. However, if there is no such hint, you have to look around the entire hall, one by one.

Look at everyone to see if there is anyone you recognize.

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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 two smaller

You may not know whether to believe him or not, but if he tells you that it breaks down to 3607 times 3803, then you can easily verify that this is true using a pocket calculator.

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It was discovered that all completely polynomial non-deterministic problems can be converted into a type of logical operation problems called satisfiability problems. Since all possible answers to such problems can be calculated in polynomial time, people then wondered whether

For this kind of problem, is there a deterministic algorithm that can directly calculate or search for the correct answer in polynomial time? This is the famous NP=P? conjecture. Regardless of whether we write the program dexterously, it is possible to determine an answer.

Quickly use internal knowledge to verify that there is still no such hint and it takes a lot of time to solve. It is regarded as one of the most outstanding problems in logic and computer science. It was stated by Steven Cock in 1971.

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Programming? Logic operations? Computer science??

Li Mo couldn't understand it. Most of the mathematical knowledge used here has not been mastered by him.

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

BSD conjecture

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

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I can't understand this question...the next one.

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

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He knows all the Chinese characters in the question, so why can’t he understand them when they are connected together?

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

.........Li Mo's face looked ugly. He remembered that he was only level 2 in mathematics. It was really difficult to use high school knowledge to try to solve an unsolved problem.

.........

Those questions whose names he couldn't understand were given up directly, and only those within the scope of high school mathematics were selected. Li Mo sped up the speed of "turning the pages".

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

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

It means that for every 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, you can eventually get 1.

Koraz's conjecture can also be called the "odd-even normalization conjecture."

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

"Positive integers", "even numbers", odd numbers. Great, very simple, completely understandable.

To think of a positive integer, let this number be

This number will eventually pass through 4,2 and become 1.

If the imagined number is 3, then it is 3×31=10, 10÷2=5, 5×31=16, 16÷2=8, 8÷2=4, 4÷2=2, 2÷2=1

.

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

Induction... doesn't work.

Using the theorem to directly prove... will not work.

Swish..swish..swish..

One piece of paper..Two pieces of paper..Three pieces of paper..

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

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

It's dawn...it's getting dark...

Still not working! Still not working!

He was a little discouraged, so he closed his eyes to rest and think 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 is a little sweet when dropped into the mouth.

It doesn't seem to be of any use...it can't be a fake.

"Wait...I thought of it...", a flash of light suddenly flashed in his brain.

n is an even number, n/2 is an even number,..., divided by 2 to 1; n is an even number, n/2 is an even number, until n divided by 2 raised to the power of X, it becomes an odd number. We divide n by 2

The power of

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n is an odd number. n

decreasing) until n(n1)/2 is an odd number.

Because: n is an odd number, and only if (n1)/2 is an even number, 1n(n1)/2 can be an odd number.

n is an odd number, n(n1)/2 is an odd number, continue below:
To be continued...