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totative : ウィキペディア英語版
totative
__NOTOC__
In number theory, a totative of a given positive integer is an integer such that and is coprime to . Euler's totient function φ(''n'') counts the number of totatives of ''n''. The totatives under multiplication modulo ''n'' form the multiplicative group of integers modulo ''n''.
The distribution of totatives has been a subject of study. Paul Erdős conjectured that, writing the totatives of ''n'' as
: 0 < a_1 < a_2 \cdots < a_ < n ,
the mean square gap satisfies
: \sum_^ (a_-a_i)^2 < C n^2 / \phi(n)
for some constant ''C'' and this was proved by Bob Vaughan and Hugh Montgomery.
==See also==

*Reduced residue system

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