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Sum divisibility !

Source: Romania TST 2015 Day 2 Problem 1

June 4, 2015
SumDivisibilitynumber theoryRomanian TSTGCD

Problem Statement

Let aa be an integer and nn a positive integer . Show that the sum :
∑k=1na(k,n)\sum_{k=1}^{n} a^{(k,n)} is divisible by nn , where (x,y)(x,y) is the greatest common divisor of the numbers xx and yy .
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