Xueba, I beg you to go and escort him quickly!

Xu Heng, "..."

"Fine!"

Instead of being committed by these people, Xu Heng went in.

"Everyone, don't add friends, I'm in the group, let's talk about it in the group!"

The group quieted down a little.

Some students suggested, "Xu Heng, let's talk about the problem-solving skills of Mathematical Olympiad! We can say that this time, it is very miserable!"

Some people also echoed, "Yes! But Yang Kaixuan said that if it were you who gave the test, the questions would be more difficult!"

"Xu Heng, what questions did you ask?"

"Let's talk about Mathematical Olympiad! Let's open our eyes!"

"After understanding the idea of ​​the topic you gave Yang Kaixuan, let us suddenly understand!"

Xu Heng, "Uh..."

There are a lot of problems.

Xu Heng, "This time, the multiple-choice questions 3,7,10, [-], and [-] for the Olympiad preliminary competition were written by me. There is no fill-in-the-blank question, but there is one for the later big question. The final finale question is also written by me."

message sent.

The group was quiet for a while.

Xu Heng is also preparing for the semi-finals and finals.

But after thinking about it, only a few people participated in the semi-finals, not to mention the finals.

So he just gave up.

The group was quiet for a while.

In the end, everyone voted unanimously, "Xu Heng, let's talk about the problem-solving skills of Mathematical Olympiad!"

"Begging for a better way!"

"From now on, the Learning Xu Heng Alliance Group is officially established!"

Originally, these people claimed to be at the top of the pyramid.

However, this pyramid is in the well!

Now that there is a chance to go up again, who wouldn't want to?

Everyone is eager to improve!

Yang Kaixuan explained from the side, "It's not me! It's really not me! They are spontaneous! They are not stupid, they have self-knowledge. Compared with you, they know where they are behind!"

Xu Heng reluctantly said, "Then let's chat casually!"

"But in fact, there is no way, just learn blindly..."

"Really..."

Xu Heng murmured while typing.

The group of people in the group couldn't hear it, but Yang Kaixuan could.

He was clutching his phone tightly!

Chilling!

Xu Heng, be yourself!

Xu Heng, "Under normal circumstances, problems with a fixed solution method or model do not belong to the Mathematical Olympiad."

"Under the guidance of the general laws of thinking, flexibly use the basic knowledge of mathematics to explore, try, choose and combine..."

"...what heuristic method, construction method, counter-evidence method, mathematical induction method, drawer principle, extreme principle, tolerance-exclusion principle..."

"The skill of Mathematical Olympiad can be regarded as the extension of mathematical skills to create new skills. You still have this thinking!"

"On the basis of it, upgrade..."

"..."

"For example, given that x, y, and z are positive numbers and xyz(x+y+z)=1, find the minimum value of the expression (x+y)(y+z)."

"Obviously 2, using the construction principle."

"The basic form of this kind is to construct a new mathematical form based on the known conditions as the raw material and the desired conclusion as the direction, so that the problem is simple and easy to solve in this situation!"

"Common, construct graphs, equations, functions, counterexamples, etc."

"Another example."

"Team A and Team B each send out 7 players to participate in the game in the order arranged in advance. The two sides will first compete with the No. 1 player, the loser will be eliminated, and the winner will then compete with the loser No. 2 player until one of the players is completely eliminated. , Seek all the possibilities of the game process."

"There are many more questions like this."

"This uses the RMI principle. It is to let R represent the relational structure of a set of preimages, or a system, which contains the preimage x to be determined, and let M represent a..."

"..."

"Acquisition, logarithmic calculation, exchange of elements, introduction of coordinate axes, construction of generating functions, design of mathematical models..."

"Forget it! That's it! This thing can't be finished all night' 々."

"Sleepy! I'm going to sleep."

Xu Heng typed very quickly, a long paragraph in a while!

The group owner also gave Xu Heng a management, and everyone was banned from speaking, only the group management could speak.

After Xu Heng finishes, unlock the silence.

On Xu Heng's side, he put down his phone and fell asleep.

But in the group, the pot exploded.

……

The next morning, Yue Pingting called Xu Heng to get up.

He stayed in bed for a few minutes, picked up his phone and looked it up.

"Fan group? Xu Heng fan alliance? What the hell? When did I have this group?"

Click in to have a look.

It's not the group from last night!

When did you become my fan group?

I was just about to ask Yang Kaixuan, but there is no one in the dormitory now.

"Hey...it's the last one again!"

Xu Heng got up, stretched, and went to wash slowly.

In class, Yue Pingting prepared breakfast.

Xu Heng asked Yang Kaixuan while eating, "What's going on in the group?"

Yang Kaixuan, "After you fell asleep, many people resonated with what you said!"

"You also know that there are some things that can only be understood and cannot be expressed, but after you say it, you still use examples to express it at your fingertips, which makes them even more admirable."

"So with the approval of the entire group, our group has become what it is now."

Xu Heng, "Uh..."

"Oh, by the way, weren't you bored before? I wanted to find some questions to pass the time. I mentioned this to them. I think, from time to time, some amazing questions will come to you."

Yang Kaixuan just finished speaking.

Group news.

"@许健大大! Look at the question!"

topic:

Proof: The cube roots of three different prime numbers cannot be three terms of an arithmetic sequence (not necessarily continuous).

The topic is very short!

Brief and concise!

But Xu Heng was not interested.

Because he still thinks this question is easy.

But in fact, for other people, although this question seems simple, it is impossible to do it.

prove?

how to prove?

Xu Heng didn't reply directly in the group, "Just saying, this question is very old."

Just when I was about to send another sentence, I politely refused.

"Ding!"

In the group, Yang Kaixuan sent a message, "This means that Xu Heng thinks it is too simple."

Xu Heng turned his head and looked at Yang Kaixuan who was secretly replying to the message.

"You bastard! Make trouble! If you are like this, I will tell the head teacher that you secretly brought your mobile phone!"

Yang Kaixuan pouted, "Don't dare next time, please let me go!"

Beware of house thieves!

Now that Yang Kaixuan has said it in the group, he doesn't need to pretend anymore.

In fact, he wanted to pretend to avoid talking in the group.

But it's better now.

Hey……

Xu Heng, "Well, that's about it."

Everyone, "%%##%..."

In private, they discussed, "Let's find a harder one!"

"We're already confused about this question, so what kind of questions are we looking for?"

"At least force Xu Heng to answer a question for us to see!"

"Too!"

"Although I saw Xu Heng analyze that physics problem while playing games last night, physics is physics, and it is still different from mathematics!"

"My heart itch, I just want to see Xu Heng do math problems!"

"+1!"

Xu Heng can also think of their general meaning.

If it wasn't for Yang Kaixuan's horizontal bar just now, Xu Heng would have already proved it.

Xu Heng hinted to himself, the following question, no matter what they send, I will directly give the problem-solving process and answer!

Probably waited until the second class was about to end.

Finally someone in the group @许娱 posted a question.

topic:

Every positive integer can be expressed as the sum of one or more consecutive positive integers. For each positive integer n, find how many different ways n can be expressed as such a sum.

This question is also very simple.

Xu Heng directly wrote down the process on the acting paper:

设m为n的正的奇因数，m=nd，则n=（d-（（m-1）/2））+…+（d-1）+d+（d+1）+…+（d+（（m-1）/2））（1）

If each item of (1) is positive, then he is a representation of n (expressed as the sum of continuous positive integers).

If there are negative numbers and 1 on the right side of formula (0), then...