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==Examples==
The easiest example of a multiplicative function is a [[monomial]]: For any particular positive integer ''n'', define ''f''(''a'') = ''a''<sup>''n''</sup>.
==Properties==
A completely multiplicative function is completely determined by its values at the prime numbers, a consequence of the [[fundamental theorem of arithmetic]]. Thus, if ''n'' is a product of powers of distinct primes, say ''n'' = ''p''<sup>''a''</sup> ''q''<sup>''b''</sup> ..., then
''f''(''n'') = ''f''(''p'')<sup>''a''</sup> ''f''(''q'')<sup>''b''</sup> ...
==See also==
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