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If integer, then square

Source: Turkey National Olympiad 2015 P1

December 14, 2015
number theoryTurkeyDivisibilityPerfect Square

Problem Statement

mm and nn are positive integers. If the number k=(m+n)24m(m−n)2+4 k=\dfrac{(m+n)^2}{4m(m-n)^2+4} is an integer, prove that kk is a perfect square.
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