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m^2 + n^2 - m is divisible by 2mn, then m is a perfect square.

Source: Switzerland - Swiss TST 1999 p6

February 19, 2020
divisiblePerfect Squarenumber theory

Problem Statement

Prove that if mm and nn are positive integers such that m2+n2āˆ’mm^2 + n^2 - m is divisible by 2mn2mn, then mm is a perfect square.
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