Euler Totient Function \(\phi(n)\) is defined as number of elements in reduced set of residues. Reduced set of residues is the numbers in a Set of residues \(Z_n = \{0, 1, \ldots, n-1\}\) which are relatively prime# to \(n\). There are several rules on computing Euler Totient Function:
$$ \begin{align} \phi(p) &= p - 1\\ \phi(n) &= \phi(p \cdot q) = (p - 1)(q - 1)\\ \phi(p^e) &= p^e - p^{e-1}\\ \phi(1) &= 1\\ \phi(n) &= \phi(a \cdot b) = \phi(a) \times \phi(b) \end{align} $$
Where:
- \(p\) and \(q\) are prime numbers