A coprime number less than a given integer
In number theory, a totative of a given positive integer n is an integer k such that 0 ; "k" ≤ "n" and k is coprime to n. 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".
Distribution.
The distribution of totatives has been a subject of study. Paul Erdős conjectured that, writing the totatives of "n" as
formula_1
the mean square gap satisfies
formula_2
for some constant "C", and this was proven by Bob Vaughan and Hugh Montgomery.
References.
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