Difference between revisions of "2005 IMO Problems/Problem 2"
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Let <math>a_1, a_2, \dots</math> be a sequence of integers with infinitely many positive and negative terms. Suppose that for every positive integer <math>n</math> the numbers <math>a_1, a_2, \dots, a_n</math> leave <math>n</math> different remainders upon division by <math>n</math>. Prove that every integer occurs exactly once in the sequence. | Let <math>a_1, a_2, \dots</math> be a sequence of integers with infinitely many positive and negative terms. Suppose that for every positive integer <math>n</math> the numbers <math>a_1, a_2, \dots, a_n</math> leave <math>n</math> different remainders upon division by <math>n</math>. Prove that every integer occurs exactly once in the sequence. | ||
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| + | ==Solution== | ||
| + | {{solution}} | ||
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| + | ==See Also== | ||
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| + | {{IMO box|year=2003|num-b=1|num-a=3}} | ||
Revision as of 23:57, 18 November 2023
Problem
Let 
be a sequence of integers with infinitely many positive and negative terms. Suppose that for every positive integer 
the numbers 
leave different remainders upon division by . Prove that every integer occurs exactly once in the sequence.
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
See Also
| 2003 IMO (Problems) • Resources | ||
| Preceded by Problem 1 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 3 |
| All IMO Problems and Solutions | ||
