Number theory · Perfect squares · Powers of two · Consecutive even numbers · Exponential vs linear bounds
Problem 5, 2021
Find all natural numbers \(n\) for which the number
\[ n \cdot 2^{n} + 4 \]
is the square of an integer.
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Serbian Regional Competition (Okruzno takmicenje) 2021, high school grade I, category A, problem 5. Organized by the Mathematical Society of Serbia (DMS). Source