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单词 Fermat Numbers
释义

Fermat Numbers

中文百科

费马数 Fermat number

(重定向自Fermat Numbers)

费马数是以数学家费马命名一组自然数,具有形式:

F_{n} = 2^{2^n} + 1

其中n为非负整数。

若2 + 1是素数,可以得到n必须是2的幂。(若n = ab,其中1 < a, b < nb为奇数,则2 + 1 ≡ (2) + 1 ≡ (−1) + 1 ≡ 0(mod 2 + 1)。)也就是说,所有具有形式2 + 1的素数必然是费马数,这些素数称为费马素数。已知的费马素数只有F0F4五个。

英语百科

Fermat number 费马数

(重定向自Fermat Numbers)

In mathematics, a Fermat number, named after Pierre de Fermat who first studied them, is a positive integer of the form

where n is a nonnegative integer. The first few Fermat numbers are:

If 2 + 1 is prime, and k > 0, it can be shown that k must be a power of two. (If k = ab where 1 ≤ a, bk and b is odd, then 2 + 1 = (2) + 1 ≡ (1) + 1 = 0 (mod 2 + 1). See below for a complete proof.) In other words, every prime of the form 2 + 1 (other than 2 = 2 + 1) is a Fermat number, and such primes are called Fermat primes. As of 2015, the only known Fermat primes are F0, F1, F2, F3, and F4 (sequence A019434 in OEIS).

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