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→Examples: the Jacobi symbol and the Legendre symbol. |
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The easiest example of a completely multiplicative function is a [[monomial]] with leading coefficient 1: For any particular positive integer ''n'', define ''f''(''a'') = ''a''<sup>''n''</sup>. Then ''f''(''bc'') = (''bc'')<sup>''n''</sup> = ''b''<sup>''n''</sup>''c''<sup>''n''</sup> = ''f''(''b'')''f''(''c''), and ''f''(1) = 1<sup>''n''</sup> = 1.
The [[Liouville function]] is a non-trivial example of a completely multiplicative function as are [[Dirichlet character]]s, the [[Jacobi symbol]] and the [[Legendre symbol]].
==Properties==
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