IMO Shortlist 2009 problem N3


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2. travnja 2012.
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Let f be a non-constant function from the set of positive integers into the set of positive integer, such that a-b divides f\!\left(a\right)-f\!\left(b\right) for all distinct positive integers a, b. Prove that there exist infinitely many primes p such that p divides f\!\left(c\right) for some positive integer c.

Proposed by Juhan Aru, Estonia
Izvor: Međunarodna matematička olimpijada, shortlist 2009