Number theory · Primes · Divisibility · Diophantine equations
A prime number \(p\) is given. Find all pairs of natural numbers \(x\) and \(y\) (positive integers) that satisfy
\[ p\,(x - 5) = x\,y . \]
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), drzavno (national) round 2003, 1. letnik, category A, problem 1. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source