CMO 2005 Problem 6

Find all nonnegative integer solutions $(x,y,z,w)$ of the equation $2^x\cdot3^y-5^z\cdot7^w=1.$

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.