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High Quality Content by WIKIPEDIA articles! In mathematics, Bertrand's postulate states that for each n 2 there is a prime p such that n p 2n. It was first proven by Pafnuty Chebyshev, and a short but advanced proof was given by Srinivasa Ramanujan. The gist of the following elementary but involved proof by contradiction is due to Paul Erd s, the basic idea of the proof is to show that a certain binomial coefficient needs to have a prime factor within the desired interval in order to be large enough. It is then shown by some extended computation that the second fact is inconsistent with the first one. Therefore Bertrand's postulate must hold. In order to present the main argument of the proof intelligibly, these lemmas and a few auxiliary claims are proved separately first.

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High Quality Content by WIKIPEDIA articles! In mathematics, Bertrand's postulate (actually a theorem) states that for each n 2 there is a prime p such that n p 2n. It was first proven by Pafnuty Chebyshev, and a short but advanced proof was given by Srinivasa Ramanujan. The gist of the following elementary but involved proof by contradiction is due to Paul Erd s, the basic idea of the proof is to show that a certain binomial coefficient needs to have a prime factor within the desired interval in order to be large enough.

Anbieter: Dodax AT

Stand: 21.01.2020 Zum Angebot

Stand: 21.01.2020 Zum Angebot

34,00 € *

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ggf. zzgl. Versand

Anbieter: Dodax

Stand: 21.01.2020 Zum Angebot

Stand: 21.01.2020 Zum Angebot