Track / Stage 5 / 331 of 400 #931 of 1964

15. 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.

I solved it I didn't Skip

Official solution

15. Prove by imitating Theorem 4.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.