The top student must be diligent

If they didn't look at Xiao Yi's method, they would never have been able to think of using these two theorems one after another.

Especially the prime number theorem, which is also part of the high school mathematics competition. For their students in Hua Luogeng's class, they basically all know this theorem. When they saw Xiao Yi use it, they seemed to be enlightened. It feels the same.

This is Xiao Shen!

"Here's the second way."

After solving the problem with the first method, Xiao Yi started another line and started writing the second method.

If the first method is a clever method, then the second method is hard evidence.

Just like Ye Cheng's hard evidence method in the previous question.

Obviously, this method looks more "showy".

With the 29 students in the class stunned, Xiao Yi almost used all the methods they had learned in mathematical analysis to the limit, and finally completed the proof of this problem.

"good!"

Ye Cheng, who was below, immediately stood up and clapped his hands violently, "As expected of me, Brother Xiao!"

The other students also reacted and clapped.

"Xiao Shen is awesome!"

Liu Bin, who was standing on the side of the podium, also smiled and clapped, walked up to the stage, and said to Xiao Yi: "Very good, very good. It seems that such a question is nothing to you."

Xiao Yi waved his hands modestly and said, "It's just that you haven't made the questions more difficult yet."

Liu Bin twitched the corner of his mouth. If this isn't difficult, how much harder do you want it to be?

Waving his hand, he said: "Okay, you can go back to your seat."

However, at this moment, Xiao Yi said: "Professor, please wait a moment. I have another method here that I want to try."

"Is there another way?" Liu Bin was stunned for a moment, then nodded: "Then you try it."

The students below were also slightly stunned.

Two methods are not enough for you?

Or even want to use a third method?

Ye Cheng: "Stand back, Brother Xiao is going to start showing off!"

…

Xiao Yi stood on the other side of the blackboard, thinking a little about the screening method that had been circulating in his mind for a long time.

Um……

I still don’t have a clue at the moment, but let’s use the sieving method to solve this problem first.

"Should I... try the Selberg sieve first?"

After thinking about it for a while, he began to write.

Chapter 94 Theoretical Materials for Building the Bridge of Truth

[Let A be the set of positive integers not greater than x, and assume that P is the set of prime numbers, and then let Ap be the set of numbers in A that are divisible by the prime number p in P...]

First of all, give the definition - this can be regarded as Xiao Yi writing this part to take care that his classmates may not understand the basic elements of the sieving method.

But in fact, his classmates really knew what the screening method was, because when they took the joint entrance examination, the questions asked by the academicians included the screening method.

Even if they didn't do it, they learned about it after they went back.

Ever since, they were all stunned.

Can this problem be solved using the sieve method?

With disbelief in their eyes, they just watched Xiao Yi continue to push forward.

[Suppose z is any real number, and P(z) is the product of prime numbers in P that are not greater than z, then we have:

S(A, P, z)=|Ap|P(z)∪Ap|……]

[Consider w(n) as the number of different prime factors of a positive integer n, introduce the above formula, and after processing, we can get...]

The students in the class either became more and more confused the more they looked at it, or the more they looked at it the more surprised they became.

It seems like this problem can really be solved in this way!

After gradually understanding the role of the sieving method in this question, they also gradually realized the ingenuity of it.

Those who have a wide range of knowledge and quick responses, such as Ye Cheng.

At this time, his expression was quite excited: "Wonderful!"

"First, use the sieving method to filter out the composite terms in w(n), determine the sequence of prime terms, and conduct separate processing, and then classify and discuss the remaining composite terms..."

"Moreover, Brother Xiao's method also avoids the parity problem in the sieve method. This sieve method... is definitely not the original Ehrlich sieve method. I visually inspected it... it should be the Selberg sieve method!"

Song Ziyang and Luo Qiao next to them were stunned.

How did your kid know?

Can you guess it visually?

It’s not like laughing and joking every day, but secretly you’re doing it better than anyone else, right?

Damn it, I must give him a good torture when I get back.

It’s okay to write the book, but it’s too inappropriate to do it secretly!

Ye Cheng never expected that he would accidentally reveal the things he usually secretly do while he was still explaining.

"It will be solved soon! Just continue to use the previous equivalent formula. With the help of the sieve method, w(n) is simply a little Karami!"

But at this moment, Ye Cheng's voice became confused: "Eh? Why did Brother Xiao stop?"

Luo Qiao and Song Ziyang were stunned.

Will Xiao Yi also stop in the process of thinking?

Is this still their Xiao Shen?

At this time, Xiao Yi in their eyes had just completed the classification of w(n) using the Selberg sieve method, and as Ye Cheng said, he had reached the final step.

But Xiao Yi's hand left the blackboard at this time, hung down, and then looked at the content on the blackboard, staying still for a long time, seemingly lost in thought.

Everyone was confused.

Some of them had already figured out the next steps, so how could Xiao Yi not figure it out?

While everyone was wondering, Xiao Yi finally raised his hand again, but he did not calculate the steps under the previous answer, but wrote in the blank space on the other side.

[A(x)A(√x)(log x)^2]

[∑_(d≤y)μ^2(d)g(d)=c1·log y+c0+O((log y)^-8)]

Lines of formulas that had nothing to do with the current question appeared on the blackboard.

Then came 30 pairs of confused eyes.

What is this?

Did they skip a period of time just now?

Why did they start writing in the heavenly book without saying anything?

"Do you understand this?" Song Ziyang poked Ye Cheng, who had just explained, and asked maliciously.

If this kid even knows this...

"I know nothing about market trade!" Ye Cheng rolled his eyes and said unhappily.

"That's good."

Then Song Ziyang breathed a sigh of relief at Ye Cheng's puzzled expression.

Ye Cheng: "I don't understand why you are so happy?"

"You don't understand." Song Ziyang smiled kindly.

...

Liu Bin on the side of the podium may be slightly better than the students below. He can probably see that what Xiao Yi wrote is still the sieving method, but from the perspective of the sieving method, his content is more advanced.

"Could this kid be..."

As a knowledgeable professor, Liu Bin had some guesses in his heart.

However, Xiao Yi, who was writing the "Heavenly Book" on the blackboard, was not so calm in his heart.

When all the inspirations that had flashed before condensed, he now realized it.

Perhaps the enlightenment in Longchang was similar?

"The biggest disadvantage of the sieve method is that there is a parity check problem."

"The parity check problem affects the sieve method's good estimation of prime number problems."

Xiao Yi thought in his heart.

"Just like the idea of ​​using the sieve method to solve this problem, we need to classify, study by category, and then break them one by one. It is undoubtedly a good idea."