MK-MO 2014 Problem 2

Solve the following equation in $\mathbb{Z}$ :

$3^{2a + 1}b^2 + 1 = 2^c$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.