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5^{2019} / \Sigma^{5^{2019}}_{k=1}3^{gcd (5^{2019},k)}

Source: Nigerian Senior Mathematics Olympiad Round 3 problem 3

September 9, 2019

number theorySumGCDgreatest common divisor

Problem Statement

Show that

5^{2019} \mid \Sigma^{5^{2019}}_{k=1}3^{gcd (5^{2019},k)}