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
the mean square gap satisfies
for some constant C and this was proved by Bob Vaughan and Hugh Montgomery.
References
Totative Wikipedia(Text) CC BY-SA