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A function f(m) is called multiplicative if (m, m') = 1 (i.e., the statement that m and m' are relatively prime) implies f(m m') = f(m) f(m') (Wilf 1994, p. 58). Examples of multiplicative functions are the Möbius function and totient function.
completely multiplicative function | Möbius function | multiplicative number theoretic function | quadratic residue | totient function
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