MathDB
Functional Equation

Source: 2012 USAMO #4

April 25, 2012
functioninductionfactorialmodular arithmeticalgebra2012 USAMOnumber theory

Problem Statement

Find all functions f:Z+→Z+f:\mathbb{Z}^+ \rightarrow \mathbb{Z}^+ (where Z+\mathbb{Z}^+ is the set of positive integers) such that f(n!)=f(n)!f(n!) = f(n)! for all positive integers nn and such that m−nm-n divides f(m)−f(n)f(m) - f(n) for all distinct positive integers m,nm, n.
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