Definition:Euler Phi Function

Let $$n \in \Z^*_+$$, that is, a positive integer.

The totient, indicator or Euler $$\phi$$-function is the function $$\phi: \Z^*_+ \to \Z^*_+$$ defined as:


 * $$\phi \left({n}\right) = $$ the number of integers less than or equal to $$n$$ which are prime to $$n$$.

That is, $$\phi \left({n}\right) = \left|{S_n}\right|: S_n = \left\{{k: 1 \le k \le n, k \perp n}\right\}$$.

Note that by this definition $$\phi \left({1}\right) = 1$$ as $$\gcd \left\{{1, 1}\right\} = 1$$.

It follows from the definition of $\Z'_n$ that $$\phi \left({n}\right)$$ is the number of elements in $$\Z'_n$$.