BALKAN-SL 2013 N3

Determine all quadruplets ( $x, y, z, t$ ) of positive integers, such that $12^x + 13^y - 14^z = 2013^t$ .

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.