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Yet another square

Source: India RMO 1992 Problem 2

October 15, 2005
number theorygreatest common divisorrelatively prime

Problem Statement

If 1a+1b=1c\frac{1}{a} + \frac{1}{b} = \frac{1}{c}, where a,b,ca,b,c are positive integers with no common factor, prove that (a+b)(a +b) is a square.
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