Track / Stage 5 / 382 of 400 #982 of 1964

Problem 982

AIME late

Number theory Difficulty 5.8 Prove it

Prove: $x^{4}+y^{2}=z^{4}$ has no solution for $x y z \neq 0$ .

This one wants a proof. Work it on paper, then read the official solution and mark yourself. Be honest about it: the record is only any use to you if it is.

Official solution

15. Prove by imitating Theorem 4.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.