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

He bowed ninety degrees all the time!

Xu Heng immediately stepped forward and helped the math teacher up.

"Teacher, teacher, teacher! Don't do this!"

"I can see that you are playing me! Including Old Sun and Old Hong."

"It's just that I didn't expect that you guys really gave me impromptu questions!"

"I also take back those words before, I hope you don't mind!"

The teacher is very excited.

Looking at Xu Heng is like looking at a treasure!

All the teachers present were also very moved.

Sudden--

The leader of the math group picked up the math problem that Xu Heng posed, and the veins on his forehead instantly popped.

"!!!"

"Ah! Ouch—"

"This, this, this, this, this... hiss! This question! This..."

Swish swish!

The teachers quickly turned their heads and gathered around to watch.

The leader of the mathematics team was already trembling and stuttered, "This question is so difficult! It's really too difficult!"

Just one look!

The leader of the mathematics team decided that Xu Heng's question was difficult!

If the topic has SSS, SS, S, A, B, C levels!

In his mind, the question given by the math teacher is A, and the question given by Xu Heng is SSS!

More than 100 teachers were all focused on the question posed by Xu Heng.

Even the old man Hongjingjun stretched his neck and stared at the topic.

topic:

Find the largest positive real number c, so that for any positive integer n, there is {(root 7)n}≥c/[(root 7)n].

Here {(root 7)n}=(root 7)n-|(root 7)n| is the non-integer part of the real number (root 7)n.

Just these two lines!

I can understand it all!

You can also understand what is the condition and what is required!

Can be combined together, all teachers do not know how to start.

The teachers of the eight subjects including Chinese, Physics, Chemistry, and Foreign Language all took two steps back.

"Give your math group room to play!"

Depend on! ! !

Play for us?

You are making it clear that you want to see our jokes!

Dear teachers, you see this question clearly!

What a difficult question!

!!!

All the teachers in the mathematics group had gloomy faces, and even their facial features were distorted.

The math teacher who came up with the question immediately looked at the leader of the math group.

The group leader was terrified.

"!!!"

"What are you looking at me for!"

He was as frightened as a bird, and then quickly cast his eyes on the Hongjing Army!

"Honglao! Honglao, take a look at this question! You..."

Before he finished speaking, Hong Jingjun shrank his neck, "I'm here to be the referee, not to help you answer the questions!"

"If you don't know, please call Xu Heng!"

Teachers, "!!!"

All the teachers in the mathematics group looked at Xu Heng in unison.

Xu Heng looked left and right.

These teachers have earnest expressions on their faces.

Xu Heng sighed resentfully, then looked at the director.

The director immediately shrunk his neck, shifted his eyes, and didn't dare to look at Xu Heng.

Xu Heng, "%#￥@￥￥￥..."

Hey!

You are the bureau chief, dare to do it or not to be it!

Xu Heng rolled his eyes.

Then, he started to solve problems on paper.

It is necessary to find the largest positive real number c, so that for any positive integer n there is (7 under the root sign) n){(7 under the root sign)n}≥c, if any positive integer n makes (7 under the root sign)n ){(root 7)n}≥c0, and there is a sequence of positive integers n1, n2,..., making the limit...

Then c0 is the largest positive real number sought.

Then for a positive integer n, record m=|(7 under the root sign)n|, and record r=7n2-m2,

Then r≥3...

"Wait a minute, student Xu Heng, your r greater than or equal to 3 is...?"

It wasn't a teacher who had doubts in his heart, even the leader of the math group was trembling and confused.

Some people even looked at the Hongjing army, and the Hongjing army immediately turned their attention to Xu Heng.

Because when Xu Heng was writing the process, he also tilted his head to look at it in a daze.

Embarrassing!

I think he is also the master of mathematics!

but--

He never expected that Xu Heng made him extremely humble when it came to this question!

许衡直接开口道，“r=7n2-m2是mod7的非平方剩余，最小的mod7非平方剩余正整数是3，所以r大于等于3。”

Non-square remainder?

Don't say that the teachers of other subjects didn't understand, even the teachers in the math group were stunned for a while before they came to their senses.

Some teachers are even immersed in thinking.

"Non-square remainder...non-square remainder, what do you mean?"

The leader of the mathematics group explained, "The square remainder is a mathematical concept. Suppose p is a prime number and a is an integer."

"If there exists an integer x such that x2≡a (i.e., x2-a is divisible by p), then a is said to be a quadratic residue in the residue class of p."

Although explained, many people still don't understand...

There are only a handful of teachers present who can understand.

Xu Heng continued.

For such m and n there are:

（根号下7）n）{（根号下7）n}=（根号下7）n）{（根号下7）n-m}=（根号下7）n*（3/（根号下7）n+m））=……

Monotonically decreasing, the tangent limit is 3/2.

Therefore, it is only necessary to prove that there are infinitely many pairs of positive integers (m, n) satisfying...

……

The process is too complicated!

It is much more complicated than the problem-solving process of the teacher's question!

The length of the process written by Xu Heng is already twice as long as the previous question!

The reverse side of a piece of paper must be filled with writing!

However, Xu Heng continued...

He continued in an orderly manner.

The more than 100 people present are in awe!

Xu Heng's pen did not stop at all.

It's like a printer.

There is no rest!

Just print!

No thinking either!

Teachers, "!!!"

They looked at each other and at all the math teachers present.

They know why other teachers are looking at them like that!

They want to ask, can you do this...

Do a fart!

do it?

how to do it !

Xu Heng is simply not human!

This is simply an answering machine!

How can we compare with him!

Anyway, after finishing writing on the front, Xu Heng slowly raised his head.

Geek!

The teachers thought that Xu Heng should have finished writing...

But in the next second, Xu Heng said, "Give me a piece of paper, there is not enough paper."

Teachers, "!!!"

Especially the math teacher who gave the question,...

Chapter 284

Xu Heng took the second piece of paper and didn't say a word. After sinking his head, he continued to write with ease.

……

（a2-7b2）（x2-7y2）=a2x2-7（a2y2+b2x2）+72b2y2

=(ax+7by)2-7(ay+bx)2