was disproved by counterexample. It asserted that at least n n^th powers were necessary to sum to another n^th power. This conjecture was disproved in 1966, with a counterexample involving n = 5; other n = 5 counterexamples are now known, as well as some n = 4 counterexamples.

Witsenhausen's counterexample shows that it is not always true (for control problems) that a quadratic loss function