Chapter 356

Chapter 359

as soon as the premier of the Wei Dynasty said with a smile, Cheng Nuo's look changed.

A paper on logical errors?

Let yourself find the logic error of mathematical language in half an hour?

Cheng Nuo frowned and thought about the difficulty of this test.

However, it is difficult for him to give an accurate conclusion before reading the whole paper.

Whether it can be completed or not, even if he is confident, he has to make a big question mark!

But at the moment, he doesn't have the option of "reject"!

Facing the smiling face of President Wei, Cheng Nuo nodded heavily, "OK, OK."

President Wei squinted, pointing to a seat in the back of the classroom, "you can answer the questions there first. We will continue to interview other students."

In half an hour, of course, it is impossible for four teachers to sit here and wait for Cheng Nuo to finish his answer.

Just take advantage of this period of time, you can interview one or two defense graduates.

Premier Wei is not worried that Cheng Nuo will use his mobile phone to search for information on the Internet.

This paper was written by him himself. Because it was a manuscript, it had never been published on any platform at all.

As for the logic error in this paper, it is even more impossible to know through abnormal means.

Everything depends on Cheng Nuo himself.

This is also the ultimate test of Cheng Nuo's mathematical level.

Although he said that even if Cheng Nuo didn't finish the answer successfully, President Wei refused to issue Cheng Nuo's diploma. However, Cheng Nuo's weight in his heart would be greatly reduced.

The allocation of follow-up research resources will also be readjusted.

Cheng Nuo took the thick paper of premier Wei and came to a seat in the back of the classroom.

In the seat drawer hole, there is a pile of draft paper and carbon pen and other stationery.

It seems that Dean Wei had planned this for a long time!

Cheng Nuo wry smile, this set whether he knew before or not, can only helplessly jump inside!

The paper has 34 pages in total, a few pages less than the paper submitted by Cheng Nuo.

papers and papers as like as two peas are all proved Bertrand hypothesis.

The only difference is that Cheng Nuo's proof method is a correct, reasonable and feasible one.

However, President Wei's is a wrong proof scheme.

Ha ha ha!

It's much better to think like this!

Cheng Nuo's mind is cleared of the haze that was calculated by Premier Wei.

He moved his fingers and kept a smile until he rubbed it, which led to a stiff face. He lowered his head and began to browse the papers of President Wei.

Attentive, he bit by bit chewed up the content of the paper.

Even the front four teachers and oral defense graduates exchange, he did not notice.

Although Wei's thesis is the same as Cheng Nuo's thesis, the specific steps are different.

In proving Bertrand's hypothesis, Cheng Nuo and chelshev, the great mathematician of the last century, both adopt the method of introducing lemma into deduction.

However, in this paper of President Wei, he took a different way of proof.

Introduction of Euler product formula!

Cheng Nuo is named after this name for the time being.

In this paper, President Wei introduced the concept of Euler product formula from the beginning of the proof process, and then deduced the proposition through the mathematical logic relationship between Euler product formula and Bertrand hypothesis.

What is Euler product formula?

If this is one of the starting points of ∑ - S = (p-1) of the complex number.

This is a rather cold mathematical formula, which is almost difficult to use in the current mathematical academic research.

I didn't expect that President Wei would suddenly think that he would use it as the other entry point to prove Bertrand's hypothesis, which is indeed worthy of being a great bull in the Chinese mathematical circle. It's just that the results don't seem perfect.

It took more than ten minutes for Cheng Nuo to read the whole paper.

Of course, this does not mean that Cheng Nuo has read the complete 34 pages of the document.

As with Cheng Nuo's graduation thesis, it's only the five or six pages.

After reading it, Cheng Nuo understood Wei's idea of proof.

First, he let f (n) be a function satisfying f (N1) f (N2) = f (N1N2), and ∑ n | f (n) | ∞ (N1 and N2 are natural numbers), then we can deduce that ∑ NF (n) = Πp [1 + F (P) + F (P2) + F (P3) +...].

After getting the above series of derivation theorems, it is the first step of proof.Next, because ∑ n | f (n) ∞, 1 + F (P) + F (P2) + F (P3) +... Is absolutely convergent. Consider the part of PN in continuous product (finite product) By using the product property of F (n), it is obtained that Π PN [1 + F (P) + F (P2) + F (P3) +...] = ∑ 'f (n).

In the third step, because 1 + F (P) + F (P2) + F (P3) +... = 1 + F (P) + F (P) 2 + F (P) 3 +... = [1-f (P)] - 1

Step four

…………

Finally, let (2n)! (n! N!) = Πp ≤ 2n3ps (P). In this paper, the continuous multiplication is divided into two parts: P ≤√ 2n and √ 2np ≤ 2n3 Therefore, Bertrand hypothesis is proved to be true.

Step by step, logical.

The idea is clear, but it seems to be in common sense.

After reading the first time, Cheng Nuo did not find any flaws in the paper.

Cheng Nuo frowned slightly.

Sure enough, it's not that simple.

Cheng Nuo didn't have time to go through it again. He first ruled out the simple part of logical deduction in the paper and ignored it directly.

If that logic error really appeared in that kind of low-level logic deduction step, Wei Yuan Yuan Yuan could not have regarded it as Cheng Nuo's thesis defense topic.

Because, that's embarrassing.

In this paper, there are five places where there are huge amount of calculation and careful derivation steps.

Cheng Nuo investigated one by one.

"The first part is the reasoning of the sum of the right end of the Euler product formula and the ordinary finite product. First, all the f (n) terms containing factor 2 at the right end of the equation are eliminated, and then..."

Second, the distribution of prime numbers and the two-step accuracy

…………

"Fourth, the substitution of the properties of F (n), f (2) ∑ NF (n) = f (2) + F (4) + F (6) +...

suddenly, Cheng Nuo, who saw this part of the content, suddenly had a glance.

He looked at the formula and looked at the corner of his mouth.

I found you!

Cheng Nuo picked up a carbon pen and wrote on the sketch paper for a while. Then he drew a horizontal line under the formula of the paper.

The formula on the horizontal line: Πp [1-f (P)] ∑ NF (n) = f (1) = 1, (2n)! (n! N!) = Πp ≤√ 2nps (P), ∑ NF (n) = Πp [1-f (P)] - 1

that's where it is, right.

There is a habitual error in the logical relationship between the third formula and the first two formulas.

These three formulas are one of the core formulas in the proof process of the whole paper. Therefore, the error of the formula leads to the whole paper becoming a waste of paper.

Cheng Nuo is in a very good mood at this time.

Because he not only found the logical error required by President Wei, but also worked out a reasonable correction plan in his mind!

Looking up, there was no one on the reply table in front of the four teachers.

Cheng Nuo picked up the paper and swaggered onto the platform.

A teacher's eyes, then a faint smile

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