Number theory · Powers of two · Difference of squares · Divisibility
Find every natural number \(n\) for which
\[ 7 \cdot 2^n + 1 \]
is a perfect square, that is, the square of an integer.
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Serbian Regional Competition (Okruzno takmicenje) 2016, high school grade I, category A, problem 1. Organized by the Mathematical Society of Serbia (DMS). Source