Content deleted Content added
No edit summary |
→Examples: consistent terminology, and spelling out the example |
||
Line 7:
==Examples==
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.
| |||