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Find all numbers satisfying a condition

Source: Turkey JBMO Team Selection Test Problem 6

May 29, 2012
number theorygreatest common divisormodular arithmeticnumber theory proposedGCD

Problem Statement

Find all positive integers m,nm,n and prime numbers pp for which 5m+2np5m−2np\frac{5^m+2^np}{5^m-2^np} is a perfect square.
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