Xu Mang was quite unlucky. He originally thought that there would be a big group behind him, not to mention thirty professors, but at least five associate professors, right?

result

A polished commander, there was only one person who set the questions for the majestic Zhejiang Provincial Mathematical Olympiad.

According to Teacher Teng, many people decided not to participate after they found out that you were the one who set the question. It would be useless to enter anyway. It was really sad to hear and made everyone cry.

In the temporary office,

Xu Mang lay on the chair, then crossed his legs, with a bottle of iced black tea beside him, and a contented expression on his face.

There are still ten days,

Don't panic!

"Hello?"

"Have you returned to the Magic City?" Xu Mang received a call from Yang Xiaoman.

"Go back tomorrow."

"Are you already at Jiangsu University?" Yang Xiaoman said, "Well, I met a lot of people, and everyone praised us, but I feel a little bit hard on my conscience. In fact, these achievements are all yours."

"It doesn't matter."

Xu Mang stretched and said silently: "I'm going to hang up and go to work."

"Um"

"Kiss me!" Yang Xiaoman said in a timid tone.

Xu Mang was stunned for a moment, then silently pressed the hangup button and looked at the interrupted call interface with a smile.

Kiss me!

Come hit me if you can?!

Work!

The first thing is the topic of the individual competition.

Since it is an individual competition, it is an occasion to show your personal strength.

Xu Mang bit the tip of his pen and kept his brows furrowed. According to international practice, the first question is to give points, and the contestants are often given some points to prevent them from losing too embarrassingly. But since changes need to be made, it is

The difficulty needs to be changed.

Submit questions?

Why is the first question worth points?

What bastard made this rule?

Xu Mang thought about it carefully and realized that there didn't need to be too many questions, as long as each question had a proposition.

The first question,

Xu Mang decided to use geometry directly!

In the convex quadrilateral abcd, ab·cd=bc·da, point x is inside the quadrilateral abcd, and angle xab=angle xcd, angle xbc=angle xda.

Prove: angle bxa + angle dxc = straight angle

"hey-hey"

"Okay, okay!" After Xu Mang finished writing the first question, he even laughed to himself, this guy is the devil!

"well"

"Xu Mang?"

"You are so handsome and smart, how can you let other young men in the world live?" Xu Mang sighed, with the word 'sad' written all over his face.

Immediately afterwards,

Xu Mang started to write the second question.

A primitive lattice point is an ordered pair of integers (x, y), where the greatest common divisor of x and y is 1. Given a finite set of primitive lattice points s, prove that there exists a positive integer n and an integer a1

,a2,a3a

n, such that for every (x, y) in s, it is true: a0x^n+a1x^n-1·y+a2x^n-2·y^2++an-1^n·xy^n

-1+an·y^n=1

(°ー°〃)Thinking~

(‵▽′)ψhehehe~

Xu Mang was happy,

This kind of question can basically be called an anti-humanity question. If you don’t have strong thinking ability and don’t understand the concept of mathematical formulas, you will definitely score zero points without looking back.

genius?

sorry,

Take at most two questions!

Xu Mang is absolutely confident in this. Regarding these two questions, Xu Mang conducted various analyzes and research based on the last two questions of the just-concluded International Mathematics Competition. It is said that this time, he failed the last two questions of the International Mathematics Competition.

Many people.

There are more than 500 people from more than 100 countries. Rumor has it that only about 10 people got it right, and about 30 people got one question right.

certainly,

The difficulty level given by Xu Mang was not at the level of the International Mathematics Competition, it was slightly lowered.

Otherwise it would be really embarrassing

"Lao Teng?"

"Isn't it a bit inappropriate to ask Xu Mang to give the question?" A professor approached the director of the Department of Mathematics of Jiangxi University and said with a worried look: "Once this guy lets himself go, the consequences will be catastrophic!"

"Don't panic!"

"Zhejiang Province is so big, I believe there will always be a second Xu Mang." Teacher Teng said: "We should be able to see it in this competition."

Facing the optimistic Teacher Teng, the professor smiled bitterly. The second Xu Mang?

"Lao Teng!"

"x^n+y^n=z^n, this theorem was proposed in 1637, but was only proved in 1995." The professor said: "It took more than three hundred years.

Here, where is the genius?”

"The Riemann Hypothesis, proposed in 1859, has not yet been solved." The professor said helplessly: "Let's talk about physics again. Modern physics is still based on the framework proposed a hundred years ago.

Research."

"Don't be superstitious about geniuses!"

"Geniuses are hard to come by." The professor said, "Hurry up and call this bastard Xu Mang back, otherwise you will really have to go out and get into trouble!"

""

Teng Lai thought for a moment and silently took out his phone.

"Hello?"

"Xu Mang, come to my office." Teacher Teng said. Mobile version::

moment,

Xu Mang came to the office with an excited face. Just now, he had completed nearly half of the individual competition papers, all of which were given for assignments.

""

""

Teacher Teng and the professor looked at each other, feeling a little panicked. This was the expression that they had just done something bad and hadn't been caught.

"Xu Mang?"

"Looking at your happy face, are you thinking about the Mathematical Olympiad topic?" Teacher Teng asked.

"Yes!"

"I have an overall idea." Xu Mang said with a smile: "This idea is great!"

""

Teacher Teng didn't know what to do for a while. His colleague's words were not unreasonable. He did not think carefully and should not leave all the tasks to Xu Mang.

"What then"

"Just now I thought about it. It's not appropriate for you to shoulder such a heavy responsibility alone." Teacher Teng said: "How about you complete the individual and team competition papers. The challenge papers are for our mathematics department.

The professor is finished?”

"What do you think?" Teacher Teng asked.

Individual competition and team competition?
To be continued...