Number theory · Divisibility · Powers and exponents · Factorisation of differences of powers · Congruences
Show that the number
\[ 2^{\,2n+3} + 3^{\,n+2}\cdot 7^{\,n} \]
is divisible by \(17\) for every natural number \(n\).
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), odbirno (qualifying) round 2018, 1. letnik, category A, problem 2. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source