Number theory · Diophantine equations · Coprime integers · Divisibility · Homogeneous equations
Problem 4, 2016
Find all pairs of coprime integers \(x\) and \(y\) that satisfy the equation
\[ 4x^{3} + y^{3} = 3xy^{2} . \]
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), drzavno (national) round 2016, 1. letnik, category A, problem B1. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source