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

"Ahem! Is it because everyone still has shadows about this year's Mathematical Olympiad? Or, after the Mathematical Olympiad is over, everyone has left the topic behind?"

The classmate's voice was so loud that it resounded throughout the classroom.

Xu Heng looked at the question intently.

topic:

Find all quaternion real arrays (x1, x2, x3, x4), so that the sum of any one of the numbers and the remaining three numbers is equal to 2.

Embarrassing!

Isn't this his topic?

Why do you always hold on to the topic of the Mathematical Olympiad?

There are several!

It's still the subject of the Mathematical Olympiad!

The previous ones were fine, but this one was made by Xu Heng.

He always felt ashamed.

Obviously such a simple question, are you still worth it?

Xu Heng can probably guess the psychology of these students.

On the one hand, it is for deliberate provocation!

On the other hand, it is because this Olympiad competition is very difficult, which refreshes their cognition, and being able to understand these questions gives them a sense of accomplishment.

"Is there no one to talk to?"

"This is just a preliminary question! I didn't have enough time for the exam before, but after I went back, I did some research and proved this proof question!"

"???"

The classmate was a little embarrassed.

He looked left and right, but no one answered his words.

It was very cold for a time!

Also very embarrassing!

The old professor who was the host also warmed up for him, "Students, don't you decide to come up and have a try?"

"Learn the new by reviewing the past..."

"..."

After a brief stalemate, some students suddenly stood up and stepped forward.

“这道题可以设x1x2x3x4=d，则xi2+d-2xi=xi（xi+（d/xi）-2）=0，所以得出。”

On the blackboard, he writes xi=1±square root (1-d) (i=1,2,3,4).

He continued, "Obviously d..."

In the end, the answer was right.

But the process is complicated.

He even fell into a misunderstanding, and it was not easy to get out of it.

After finishing this question, the student walked down slowly.

"Crash..."

Then there was applause.

At this time, Yang Kaixuan and He Junfei approached Xu Heng and asked, "How to do this question is good, but I always feel that it is a bit complicated. Xu Heng, do you have any simpler ideas?"

Xu Heng shook his head.

He Junfei clenched his fists. "Then isn't this giving them the limelight for nothing?"

Xu Heng smiled, "Although the method is the same, but his verification process is a bit more complicated, especially where on the second blackboard, it is obviously possible..."

Xu Heng pointed out the problem directly.

At this time, the host looked at the audience, "What do you guys think of the proof of this question? Does anyone have any different opinions and suggestions?"

"Everyone, don't be nervous, and don't feel embarrassed. This exchange meeting is to promote mutual learning and integration, and everyone can speak freely."

The voice fell.

ten seconds...

20 second……

No classmates came forward again.

The host frowned slightly, and pushed his thick glasses, "Since there are no, then let's move on to the next..."

Shout it!

He Junfei got up suddenly, and under the attention of everyone, he walked to the blackboard with strides.

Picking up the blackboard eraser, he directly erased part of the other student's problem-solving ideas.

"!!!"

clap la la...

There was an uproar.

Especially the corner of that classmate's eyes was twitching hard, and the area that was wiped off was the step he was most proud of.

Because at this point, many students will fall into misunderstandings and cannot continue to prove.

Only he got out.

He was just about to get up.

He Junfei said bluntly, "It's too complicated! Although the idea of ​​this question is correct, most of the students have fallen into misunderstandings."

"Here! Everyone, please see, since there are five situations."

He Junfei quickly wrote:

第一种情况，x1=x2=x3=x4=1+根号下（1-d），则d=（1+根号下（1-d））4次方≥1≥d，所以，d=1，x1x2x3x4=1.

"Directly push back, according to..."

"We're looking at the second scenario!"

第二种情况，x1、x2、x3、x4中有三个为1+根号下（1-d），一个为1-根号下（1-d），则d=（1-根号下（1-d））（1+根号下（1-d））3=d（1+根号下（1-d）2），所以d=0，从而x1、x2、x3、x4中三个为2，一个为0，但0+2*2*2≠2，所以d=0，是不可能的.

"Based on this, we can directly deny the second case. If we follow what the previous classmate said, it will be too convoluted! And it is very likely to make mistakes!"

The sound is loud!

He Junfei's direct and sharp words made everyone look sideways.

The other two provinces gasped, "It seems that after they came back from the province, they must have learned from the pain! They studied the Olympiad competition questions well."

The leading teachers of these two provinces looked sideways at Xu Heng.

They are a little curious.

"If I remember correctly, there were 56 of them going to participate in the Math Olympiad. How come there are 57 of them here today?"

"Is this classmate a senior in high school?"

That's all they can understand.

If Xu Heng is the trump card, why didn't he use it earlier in the competition, and had to wait until the exchange meeting?

"I don't think it's very possible, not to mention the task of the third year of high school. If the student really has good grades, then he will naturally be recommended."

"If you are recommended, you will have more free time. Why don't you participate in the Mathematical Olympiad?"

Several teachers muttered.

"By the way, do you think that classmate is familiar? I always feel that I have seen him somewhere?"

"You mean, he participated in the Olympiad competition?"

"No, no, no! No, it's somewhere else! But I can't remember it for a while."

This is a mathematics exchange meeting. These teachers' preconceived ideas are naturally related to mathematics, so they don't think about other aspects at all, and literature is even more thrown out of the sky.

Several teachers stared at Xu Heng.

When they looked at the blackboard again.

Can't help the corners of his eyes twitching.

On the blackboard, the proof ideas written by He Junfei were half as long as the previous classmate's!

Intuitive!

concise!

understand!

He Junfei, "The above are the five situations!"

“综上所述，x1、x2、x3、x4或者全为1，或者其中有三个为-1，一个为3！”

After finishing speaking, He Junfei started to erase the questions on the blackboard...

"!!!"

"What are you doing?! This classmate!"

It's not just the host who is in a hurry, but many students present are nervous.

He Junfei was stunned for a moment, and said calmly, "Erase it! I want to share the topic with everyone!"

On the surface it says so!

But in fact, this is Xu Heng's request.

Go up and get it done quickly, and then erase my question!

He Junfei fulfilled his mission!

Everyone was stunned, and the question was erased.

Then, his topic was on the blackboard.

topic:

Let a1, a2, ... be an infinite sequence, there is always an integer N>1, so that for each integer n≥N,

（a1/a2）+（a2/a3）+…+（a（n-1）/an）+（an/a1）

They are all integers. Prove that there is a positive integer M such that am=a(m+1) is true for all integers m≥M.

He Junfei, "Don't be obsessed with the past! By analogy, the key is to look to the future!"

In a word, it refuted the obsession of the previous students with the Mathematical Olympiad.

"Please teach me, my classmates!"

"Just 10 minutes..."

"Hey! 10 minutes is too long! After all, some students in our province don't bother to look at these questions!"

You are all secretly provoking!

And we!

I don't pretend anymore!

We have the strong backing of Xu Heng, what are we afraid of?

One person is enough to instantly kill more than 100 people in your two provinces!

He Junfei speaks with confidence!

After writing the question, he walked down.

Whether it is the host or the leader of the Education Bureau.

They haven't seen such an "arrogant" classmate for a long time!