Number theory · Primes · Divisibility · Diophantine equations
Find all prime numbers \(p\), \(q\) and \(r\) for which
\[ 15p + 7pq + qr = pqr . \]
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), izbirno (selection) round 2010, 1. letnik, category A, problem 2. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source