Number theory · Fermats little theorem · Units digits · Modular arithmetic · Compositeness
Prove that there is a natural number \(n\) for which the number
\[ 2p^{n} + 3 \]
is composite for every prime number \(p\).
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Serbian National Competition (Drzavno takmicenje) 2008, high school grade I, category A, problem 5. Organized by the Mathematical Society of Serbia (DMS). Source