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Hidden elliptic curve in a junior level problem

Source: 4th Memorial Mathematical Competition "Aleksandar Blazhevski - Cane"- Junior D2 P4

December 21, 2022
number theoryJuniorconstruction

Problem Statement

Does the equation z(yāˆ’x)(x+y)=x3z(y-x)(x+y)=x^3 have finitely many solutions in the set of positive integers?
Proposed by Nikola Velov
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