Number theory · Divisibility · Primes · Perfect squares · Difference of squares
Find all natural numbers \(n\) and all primes \(p\) for which
\[ \sqrt{\,n + \frac{p}{n}\,} \]
is a natural number.
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), regijsko (regional) round 2012, 1. letnik, category A, problem B2. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source