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Infinite sets

Source: RMO 2008, Grade 10, Problem 4

April 30, 2008
number theorynumber theory proposed

Problem Statement

We consider the proposition p(n) p(n): n^2\plus{}1 divides n! n!, for positive integers n n. Prove that there are infinite values of n n for which p(n) p(n) is true, and infinite values of n n for which p(n) p(n) is false.
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