Numbers not Expressible as Sum of Fewer than 19 Fourth Powers/Historical Note

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Historical Note on Numbers not Expressible as Sum of Fewer than 19 Fourth Powers

It was noted by Leonard Eugene Dickson that there are no other positive integers less than $4100$ needing $19$ fourth powers to express them.

This limit was reported by David Wells in his Curious and Interesting Numbers of $1986$.

Jean-Marc Deshouillers, François Hennecart and Bernard Landreau extended this to $10^{245}$ in $2000$.

In $2005$, Koichi Kawada, Trevor Dion Wooley and Jean-Marc Deshouillers showed that the sequence is complete beyond $10^{220}$.


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