Number theory · Diophantine equations · Quadratic forms · Sums of squares · Integer solutions
Problem 2, 2001
Find all pairs of integers \(x\) and \(y\) that satisfy the equation
\[ x^2 + xy + y^2 = 1 . \]
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), izbirno (selection) round 2001, 1. letnik, category A, problem 2. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source