totativeTotative2007-04-23 11:36:052007-05-08 15:37:00Definition% this is the default PlanetMath preamble. as your knowledge
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Given a positive integer $n$, an integer $0 < m < n$ is a {\em totative} of $n$ if $\gcd(m, n) = 1$. Put another way, all the smaller integers than $n$ that are coprime 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 $\phi(n)$. The set of totatives of $n$ forms a reduced residue system 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).