Number theory · Diophantine equations · Unit fractions · Divisors of an integer
Find all natural numbers \(m\) and \(n\) that satisfy
\[ \frac{3}{m} + \frac{5}{n} = 1 . \]
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), izbirno (selection) round 2004, 1. letnik, category A, problem 1. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source