MEMO 2012 Problem 7

Find all triplets $(x,y,z)$ of positive integers such that $x^y + y^x = z^y$ $x^y + 2012 = y^{z+1}$

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.