Number theory · Divisibility · Coprimality · Diophantine equations
Determine every pair of coprime natural numbers \(m\) and \(n\) for which
\[ \frac{5m - n}{m + n} \]
is itself a natural number. (Here the natural numbers are the positive integers \(1, 2, 3, \ldots\).)
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), drzavno (national) round 2006, 1. letnik, category A, problem 2. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source