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Bosnia and Herzegovina JBMO TST 2011 Problem 1

Source: Bosnia and Herzegovina Junior Balkan Mathematical Olympiad TST 2011

September 16, 2018

positive integernumber theoryequation

Problem Statement

Solve equation

\frac{1}{x}-\frac{1}{y}=\frac{1}{5}-\frac{1}{xy}

, where

x

and

y

are positive integers.