Number theory · Primes · Difference of squares · Divisibility · Modular arithmetic
Problem 4, 2018
Find all prime numbers \(p\), \(q\) and \(r\) that satisfy
\[ r^{4} = pq + 4 . \]
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), drzavno (national) round 2018, 1. letnik, category A, problem B1. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source