Euler's Sum of Powers Conjecture

Euler conjectured that at least $n$ $n$th Powers are required for $n>2$ to provide a sum that is itself an $n$th Power. The conjecture was disproved by Lander and Parkin (1967) with the counterexample

$$27^5+84^5+110^5+133^5=144^5.$$

See also Diophantine Equation

References

Lander, L. J. and Parkin, T. R. ``A Counterexample to Euler's Sum of Powers Conjecture.'' Math. Comput. 21, 101-103, 1967.