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Euclid–Euler theorem : ウィキペディア英語版 | Euclid–Euler theorem The Euclid–Euler theorem is a theorem in mathematics that relates perfect numbers to Mersenne primes. It states that every even perfect number can be represented by the form 2''n'' − 1(2''n'' − 1), where 2''n'' − 1 is a prime number. The prime numbers of this form are known as Mersenne primes, and thus require ''n'' itself to be prime. ==Statement== An even positive integer is a perfect number, that is, equals the sum of its proper divisors, if and only if it has the form 2''p''−1''M''''p'' where ''M''''p'' is a Mersenne prime (i.e. a prime number of the form ''M''''p'' = 2''p'' − 1).〔.〕
抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)』 ■ウィキペディアで「Euclid–Euler theorem」の詳細全文を読む
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