Euler's Sum of Powers Conjecture/Historical Note

Historical Note on Euler's Sum of Powers Conjecture

This was proven false by the counterexample found by Leon J. Lander and Thomas R. Parkin in $1966$, when they were using a computer to hunt for $5$th powers which were the sum of $5$ $5$th powers.

In one of the $4$ solutions they found, one of the contributing $5$th powers was $0^5$.

It was at that point it was realised that here was a counterexample to Euler's Sum of Powers Conjecture.


Since then, further counterexamples have been found, for various powers.


Sources

  • 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $144$
  • 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $144$
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