2005 IMO Problems/Problem 2

Problem

Let $a_1, a_2, \dots$ be a sequence of integers with infinitely many positive and negative terms. Suppose that for every positive integer $n$ the numbers $a_1, a_2, \dots, a_n$ leave $n$ different remainders upon division by $n$ . Prove that every integer occurs exactly once in the sequence.

Solution

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2005 IMO (Problems) • Resources
Preceded by Problem 1	1 • 2 • 3 • 4 • 5 • 6	Followed by Problem 3
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2005 IMO Problems/Problem 2

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