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1

Part of 2015 Turkey MO (2nd round)

Problems(1)

If integer, then square

Source: Turkey National Olympiad 2015 P1

12/14/2015
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.
number theoryTurkeyDivisibilityPerfect Square