Given a positive integer n, an integer 0<m<n is a totativeMathworldPlanetmath of n if gcd(m,n)=1. Put another way, all the smaller integers than n that are coprimeMathworldPlanetmath to n are totatives of n.

For example, the totatives of 21 are 1, 2, 4, 5, 8, 10, 11, 13, 16, 17, 19 and 20.

The count of totatives of n is Euler’s totient function ϕ(n). The set of totatives of n forms a reduced residue systemMathworldPlanetmath modulo n. The word “totative” was coined by James Joseph Sylvester, who also coined “totient” (though despite occasional usage in some papers and books, the term “totative” has not caught on the way “totient” has).

Title totative
Canonical name Totative
Date of creation 2013-03-22 16:58:16
Last modified on 2013-03-22 16:58:16
Owner CompositeFan (12809)
Last modified by CompositeFan (12809)
Numerical id 9
Author CompositeFan (12809)
Entry type Definition
Classification msc 11A25
Related topic ResidueSystems