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Product of Consecutive Integers

Source: USAMO 2008 Problem 1

May 1, 2008
trigonometrycalculusintegrationmodular arithmeticinductionalgebrapolynomial

Problem Statement

Prove that for each positive integer n n, there are pairwise relatively prime integers k0,k1,…,kn k_0,k_1,\ldots,k_n, all strictly greater than 1 1, such that k_0k_1\ldots k_n\minus{}1 is the product of two consecutive integers.
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