# Difference between revisions of "2012 USAMO Problems/Problem 4"

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== Problem == | == Problem == | ||

− | + | Find all functions <math>f : \mathbb{Z}^+ \to \mathbb{Z}^+</math> (where <math>\mathbb{Z}^+</math> is the set of positive integers) such that <math>f(n!) = f(n)!</math> for all positive integers <math>n</math> and such that <math>m - n</math> divides <math>f(m) - f(n)</math> for all distinct positive integers <math>m</math>, <math>n</math>. | |

==Solution== | ==Solution== |

## Revision as of 17:54, 25 April 2012

## Problem

Find all functions (where is the set of positive integers) such that for all positive integers and such that divides for all distinct positive integers , .