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Find the greatest comon divisor of the numbers A_1,..,A_1999

Source: JBMO 1999, Problem 2

October 30, 2005
modular arithmeticnumber theorygreatest common divisor

Problem Statement

For each nonnegative integer nn we define An=23n+36n+2+56n+2A_n = 2^{3n}+3^{6n+2}+5^{6n+2}. Find the greatest common divisor of the numbers A0,A1,…,A1999A_0,A_1,\ldots, A_{1999}. Romania
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