MathDB

triples (x,y,z) in Q+

Source: Problem 1, Polish NO 1994

October 7, 2005

algebrapolynomialRational Root Theoremalgebra unsolved

Problem Statement

Find all triples

(x,y,z)

of positive rationals such that

x + y + z

\dfrac{1}{x} + \dfrac{1}{y} + \dfrac{1}{z}

and

xyz

are all integers.