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 
, .
