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Different definitions exist depending on the specific field of application. Traditionally, an '''additive function''' is a function that preserves the addition operation:
:''f''(''x''+''y'') = ''f''(''x'')+''f''(''y'').
In [[number theory]], an '''additive function''' is an [[arithmetic function]] ''f''(''n'') of the positive [[integer]] ''n'' such that whenever ''a'' and ''b'' are [[coprime]] we have:
:''f''(''ab'') = ''f''(''a'') + ''f''(''b'').
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