The conjecture was disproved by L. J. Lander and T. R. Parkin in 1966 when they found the following counterexample for *n* = 5:

- 27
^{5}+ 84^{5}+ 110^{5}+ 133^{5}= 144^{5}.

In 1988, Noam Elkies found a method to construct counterexamples for the *n* = 4 case. His smallest counterexample was the following:

- 2682440
^{4}+ 15365639^{4}+ 18796760^{4}= 20615673^{4}.

Roger Frye subsequently found the smallest possible *n* = 4 counterexample by a direct computer search using techniques suggested by Elkies:

- 95800
^{4}+ 217519^{4}+ 414560^{4}= 422481^{4}.

No counterexamples for *n* > 5 are currently known.