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) = an. Then f(bc) = (bc)n = bncn = f(b)f(c), and f(1) = 1n = 1.
The Liouville function is a non-trivial example of a completely multiplicative function as are Dirichlet characters.
Read more about this topic: Completely Multiplicative Function
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