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(n^3 -n)(5^{8n+4} +3^{4n+2}) is a multiple of 3804

Source: 1st Mexican Mathematical Olympiad 1987 OMM P6

July 27, 2018
number theorydivisor

Problem Statement

Prove that for every positive integer n the number (n3āˆ’n)(58n+4+34n+2)(n^3 -n)(5^{8n+4} +3^{4n+2}) is a multiple of 38043804.
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