Number theory · Factorisation · Powers of two · Parity · Diophantine equations
Determine all pairs of positive integers \(a\) and \(b\) for which the number
\[ a^4 b + 3b - 2a^2 b^2 - a^2 - 3b^3 \]
is a power of two.
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Serbian National Competition (Drzavno takmicenje) 2017, high school grade I, category A, problem 2. Organized by the Mathematical Society of Serbia (DMS). Source