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A diophantine equation

Source: Turkey Junior National Olympiad 2012 P1

December 12, 2012
quadraticscalculusintegrationnumber theoryDiophantine equationnumber theory proposed

Problem Statement

Let x,yx, y be integers and pp be a prime for which
x2āˆ’3xy+p2y2=12p x^2-3xy+p^2y^2=12p Find all triples (x,y,p)(x,y,p).
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