Chapter 347 (1/2)

Chapter 350

on the other side, China.

After a night of thinking, perplexed Cheng Nuo finally has a new idea for his graduation thesis.

Cheng Nuo has his own unique views on the application of the two lemmas.

So, as soon as the day's class was over, Cheng Nuo rushed to the library, picked a place where no one was, took out a pen and paper, and verified his ideas.

Since it doesn't work to force two lemmas into the proof of Bertrand's hypothesis, what Cheng Nuo thinks is whether he can draw some inferences according to these two lemmas and then apply them to Bertrand hypothesis.

In this way, although turning a corner, it seems to be more troublesome than Chebyshev's method. But before the real results come out, no one dares to say so.

Cheng Nuo thinks we should try it.

The tools were already ready. He pondered for a while and began to make various attempts on the draft paper.

Whether he is God or not, he can't clearly know which inference is useful and which is not. The surest way is to try one by one.

Anyway, time is enough, Cheng Nuo is not in a hurry.

Shua Shua Shua ~ ~

with his head down, he lists the next line of arithmetic.

Let m be the largest natural number satisfying PM ≤ 2n, then obviously for I &; m, floor (2npi) - 2floor (NPI) = 0-0 = 0, the summation stops at I = m, and there are m terms. Since floor (2x) - 2floor (x) ≤ 1, every term in the M term is either 0 or 1 】

from above, we can infer 1: [if n is a natural number and P is a prime number, then the highest power of P that can be divisible by (2n)! (n! N!) is s = ∑ I ≥ 1 [floor (2npi) - 2floor (NPI)]. 】

[because n ≥ 3 and 2n3 & & P ≤ n indicate that P2 &; 2n, there is only one term I = 1, that is, s = floor (2np) - 2floor (NP). Since 2n3 & & P ≤ n also indicates 1 ≤ NP & & 32, s = floor (2np) - 2floor (NP) = 2-2 = 0. 】Let n ≥ 3 be a natural number, p be a prime number, s be the highest power of P that can be divisible by (2n)! (n! N!), then: (a) PS ≤ 2n; (b) if P - &; √ 2n, then s ≤ 1; (C) if 2n3 & & P ≤ n, then s = 0. 】

, a row.

Besides class, Cheng spent the whole day in the library.

When the library closes at 10 o'clock in the evening, Cheng Nuo leaves with his schoolbag on his back.

And in his hand holding on the draft paper, has a dozen inference.

This is the result of a day's work.

Tomorrow, Cheng Nuo's work is to find out from these more than ten inferences useful for Bertrand's hypothesis proof work.

…………

There was no word all night.

The next day, it was a sunny day with spring flowers.

The date is early March. Professor Fang has more than ten days left in his one month vacation.

Cheng Nuo has enough time to go to the waves Oh, no, to perfect his thesis.

The progress of the paper is carried out according to the plan of Cheng Nuo's plan. On this day, he found five corollaries which prove the important role of Bertrand hypothesis from more than ten inferences.

After a busy day, Cheng Nuo began to prove Bertrand's hypothesis.

It's not an easy job.

Cheng Nuo is not sure that he can finish it in a day.

But as an old saying goes, keep up one's spirits, decline again, and exhaust three times. Now the momentum is enough, the best day to win.

At this time, Cheng Nuo had to prepare to open the immortal cultivation method again.

Cheng Nuo has already prepared the Shenbao, the artifact of cultivating immortals.

Liver, boy!

Cheng Nuo's right hand carbon pen, left hand kidney treasure, began to overcome the last hurdle.

In proving Bertrand's hypothesis, cherchev's scheme is to directly carry out the known theorem and carry out rigid derivation without any skill at all.

Cheng Nuo certainly can't do that.