Number theory · Diophantine equations · Unit fractions · Divisors · Extraneous solutions
Determine every pair of integers \((x, y)\) for which
\[ \frac{1}{x} + \frac{1}{y} = \frac{1}{2} . \]
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), izbirno (selection) round 2002, 1. letnik, category A, problem 2. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source