AMO-Bench 2025 Problem 26

Find the number of positive integer solutions $(x, y, z)$ to the equation $x^{999} + y^{1000} = z^{1001}.$

Dataset text AMO-Bench. Open licence.

Show the answer

Infinitely many. \textit{(Note: any answer conveying ``infinite'' is accepted.)}

Solutions

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