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Find gcd(5^m+7^m,5^n+7^n) for coprime m,n

Source: Japanese MO Finals 1996

February 11, 2011
number theorygreatest common divisornumber theory proposed

Problem Statement

Let m,nm,n be positive integers with (m,n)=1(m,n)=1. Find (5m+7m,5n+7n)(5^m+7^m,5^n+7^n).
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