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Diophantine - Coprime - Infinite solutions proof

Source: ILL 1979 - Problem 55

June 5, 2011
number theorygreatest common divisorsearchrelatively primenumber theory unsolved

Problem Statement

Let a,ba,b be coprime integers. Show that the equation ax2+by2=z3ax^2 + by^2 =z^3 has an infinite set of solutions (x,y,z)(x,y,z) with {x,y,z}āˆˆZ\{x,y,z\}\in\mathbb{Z} and each pair of x,yx,y mutually coprime.
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