\(\qquad\)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 \(a_1, a_2, \ldots\), an leave \(n\) different remainders upon division by \(n\). \(\\\qquad\)Prove that every integer occurs exactly once in the sequence \(a_1, a_2, \ldots\).
| Attributes | Олімпіадна |
|---|---|
| Source | International Mathematical Olympiad |
| Year | 2005 |
| Number | 2 |
| Difficulty | 10.0 |
| Themes |