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rational number theory

Source: Yugoslav TST 1995 P1

May 27, 2021
number theoryrational numberrationalrational numbers

Problem Statement

Determine all triples (x,y,z)(x,y,z) of positive rational numbers with x≤y≤zx\le y\le z such that x+y+z,1x+1y+1zx+y+z,\frac1x+\frac1y+\frac1z, and xyz are natural numbers.
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