Number theory · Divisibility · Prime factorisation · Diophantine pairs · Euclid lemma
Find all pairs of natural numbers \(m\) and \(n\) whose sum equals \(2007\) and whose product is divisible by \(2007\).
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), drzavno (national) round 2007, 1. letnik, category A, problem 2. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source