Algebra · Diophantine equations · Factoring · Quadratic inequalities · Integer solutions
The integers \(x\) and \(y\) satisfy
\[ x + xy + y^{2} = 1 \qquad\text{and}\qquad y(5 + x) \ge 0 . \]
Which integer values can the expression \(x - y\) take?
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), drzavno (national) round 2012, 1. letnik, category A, problem 2. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source