IMO Shortlist 2005 problem N2


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2. travnja 2012.
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Let a_1,a_2,\ldots be a sequence of integers with infinitely many positive and negative terms. Suppose that for every positive integer n the numbers a_1,a_2,\ldots,a_n leave n different remainders upon division by n.

Prove that every integer occurs exactly once in the sequence a_1,a_2,\ldots.
Izvor: Međunarodna matematička olimpijada, shortlist 2005