Chapter 442 (2/2)

”Well, Cheng Nuo, can you tell me again?” The student in charge of the record scratched his head and said in a slightly embarrassed way, ”I just patronized stupidly and forgot to record.”

Cheng Nuo shrugged helplessly, ”OK, I'll say it again. You should listen carefully this time.”

The fire light of the campfire reflected on Cheng Nuo's side face, showing incomparable brilliance.

Cheng Nuo's two doctoral students nodded together as if they were good babies, with an open-minded attitude of being taught.

“…… The sixth is to prove it by topological method

The two men were immediately suspicious.

Cheng Nuo noticed their puzzled eyes and laughed, ”I understand your doubts. Topology and number theory seem to be two fields that I don't want to do. Why do I say that. When I'm done, you'll know. ”

”We can define a topology on the set of integers whose open set consists of and only the union of the empty set ℤ and the arithmetic sequence a ???? B (a ≠ 0 and B are integers). It is not difficult to prove that the open set defined in this way satisfies the definition of topology, i.e.,.... ”

“…… From this, we know that there are infinitely many primes. Do you understand now? ”

Two people together, chicken peck rice nod, brain constantly aftertaste Cheng Nuo's words.

But Cheng Nuo didn't leave them too much time for aftertaste.After a brief thought in his mind, Cheng Nuo tells the next proof.

Now half an hour has almost passed. If you don't grasp the time, you may not be able to finish it.

”The seventh one is to prove the application of prime numbers in information, coding and other fields. The process is very simple, and the positive integer n can be decomposed into the continuous product of prime numbers: n = p1m1 · p2m2... ”

” Eighth, by using the direction of the function, Let f (n) be the number of different prime numbers divisible by N. if there are only a finite number of primes and the product of them is p, it is obvious that for all n there is f (n) = f (n + P)... ”

“…… The ninth, I call it the single line proof of prime numbers. The single line expression is: 0 ＜ Π sin (π P) = Πsin (π (1 + 2 Π p ') P), assuming that there are only a finite number of prime numbers. If there are only a finite number of primes, then all the independent variables π P of sin in the product of left ”” and right end of the expression are all between 0 and π, sin (π P); 0,...... ”

”Hoo Hoo -!”

After finishing the ninth proof, Cheng Nuo felt thirsty and poured down the remaining half bottle of mineral water.

A person is very witty and handed Cheng Nuo a bottle of mineral water.

Seeing that Cheng Nuo had no action for a long time, the student who was in charge of recording turned over his four page formula, swallowed his saliva and asked carefully, ”is there anything else?”

Cheng Nuo waved his hand and said with a wry smile, ”the only proof I can think of in the new direction is these nine. Alas, it's too far away from more than 500 proof methods of Pythagorean theorem.”

Cheng Nuo smiles bitterly, and they also smile bitterly.

There are more than 500 kinds of proofs of Pythagorean theorem, but they have been formed after thousands of years of history and the development of dozens of generations of mathematicians.

Cheng Nuo can come up with nine proofs of infinite prime in less than half an hour, which is beyond the scope of their understanding.

Can listen to Cheng Nuo's tone, he seems quite dissatisfied.

This

What else can they say!