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Diophantine equation

Source: Greek olympiad - 2006 , senior level, Baltic Way 2002

February 25, 2006
modular arithmeticnumber theory proposednumber theory

Problem Statement

Let nn be a positive integer. Prove that the equation x+y+1x+1y=3nx+y+\frac{1}{x}+\frac{1}{y}=3n does not have solutions in positive rational numbers.
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