# Totative

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*.

## DistributionEdit

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 proven by Bob Vaughan and Hugh Montgomery.^{[1]}

## See alsoEdit

## ReferencesEdit

**^**Montgomery, H.L.; Vaughan, R.C. (1986). "On the distribution of reduced residues".*Ann. Math*. 2.**123**: 311–333. doi:10.2307/1971274. Zbl 0591.10042.

- Guy, Richard K. (2004).
*Unsolved problems in number theory*(3rd ed.). Springer-Verlag. B40. ISBN 978-0-387-20860-2. Zbl 1058.11001.

## Further readingEdit

- Sándor, Jozsef; Crstici, Borislav (2004),
*Handbook of number theory II*, Dordrecht: Kluwer Academic, pp. 242–250, ISBN 1-4020-2546-7, Zbl 1079.11001

## External linksEdit

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