2005 IMO Problems/Problem 2

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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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See Also

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