Number theory · Primes · Parity · Modular arithmetic · Divisibility
Determine all prime numbers \(p\) and \(q\) for which the number
\[ 2^{2} + p^{2} + q^{2} \]
is also prime.
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), drzavno (national) round 2011, 1. letnik, category A, problem 1. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source