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Consecutive integers, none divisible by n, whose product is

Source: XVII Tuymaada Mathematical Olympiad (2010), Senior Level

July 31, 2011
number theory unsolvednumber theory

Problem Statement

For a given positive integer nn, it's known that there exist 20102010 consecutive positive integers such that none of them is divisible by nn but their product is divisible by nn. Prove that there exist 20042004 consecutive positive integers such that none of them is divisible by nn but their product is divisible by nn.
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