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An Old-Style Cubic Diophantine Equation

Source: Germany 2022, Problem 4

June 25, 2022
number theorynumber theory proposedDiophantine equationDiophantine Equationscubic equation

Problem Statement

Determine all 66-tuples (x,y,z,u,v,w)(x,y,z,u,v,w) of integers satisfying the equation x3+7y3+49z3=2u3+14v3+98w3.x^3+7y^3+49z^3=2u^3+14v^3+98w^3.
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