“totient function”的概念、定义、习题解题方法及翻译-数学辞典

单词

totient function

释义

totient function

(Euler's phi function) For a positive integer n, let ϕ(n) be the number of positive integers less than n that are coprime to n. For example, ϕ(12) = 4, since four numbers, 1, 5, 7, and 11, are coprime to 12. This function ϕ, defined on the set of positive integers, is the totient function. It can be shown that, if the prime decomposition of n is $inline$ , then

Euler proved the following extension of Fermat's Little Theorem: if n is a positive integer and a is any integer such that (a, n) = 1, then a ϕ(n) ≡ 1 (mod n). The totient function is an arithmetic function.

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