The conjecture was disproved by L. J. Lander[?] and T. R. Parkin[?] in 1966 when they found the following counterexample for n = 5:
In 1988, Noam Elkies[?] found a method to construct counterexamples for the n = 4 case. His smallest counterexample was the following:
Roger Frye[?] subsequently found the smallest possible n = 4 counterexample by a direct computer search using techniques suggested by Elkies:
No counterexamples for n > 5 are currently known.
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