翻訳と辞書 
Fermat prime A {prime number} of the form 2^2^n + 1. Any prime number of the form 2^n+1 must be a Fermat prime. {Fermat} conjectured in a letter to someone or other that all numbers 2^2^n+1 are prime, having noticed that this is true for n=0,1,2,3,4. Euler proved that 641 is a factor of 2^2^5+1. Of course nowadays we would just ask a computer, but at the time it was an impressive achievement (and his proof is very elegant). No further Fermat primes are known; several have been factorised, and several more have been proved composite without finding explicit factorisations. Gauss proved that a regular Nsided {polygon} can be constructed with ruler and compasses if and only if N is a power of 2 times a product of distinct Fermat primes. (19950410)
スポンサード リンク
翻訳と辞書 : 翻訳のためのインターネットリソース 
Copyright(C) kotoba.ne.jp 19972016. All Rights Reserved.

