Number theory · Greatest common divisor · Least common multiple · Divisibility · Coprime cofactors
Let \(d\) denote the greatest common divisor and \(v\) the least common multiple of the natural numbers \(m\) and \(n\). Prove that if
\[ 3m + n = 3v + d , \]
then \(n\) divides \(m\).
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), izbirno (selection) round 2001, 1. letnik, category A, problem 1. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source