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Two Quadratics have Integer Roots

Source: Indian RMO 2013 Paper 1 Problem 6

February 1, 2014
quadraticsmodular arithmeticnumber theoryDiophantine equationnumber theory unsolved

Problem Statement

Suppose that mm and nn are integers, such that both the quadratic equations x2+mx−n=0x^2+mx-n=0 and x2−mx+n=0x^2-mx+n=0 have integer roots. Prove that nn is divisible by 66.
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