Hilbert-Waring Theorem/Variant Form/Particular Cases/4/Historical Note
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Particular Case of the Hilbert-Waring Theorem -- Variant Form: $k = 4$: Historical Note
Harold Davenport showed in $1939$ that $G \left({4}\right) = 16$.
$13792$ is the largest number to require $17$ fourth powers.
Jean-Marc Deshouillers, François Hennecart and Bernard Landreau showed in $2000$ that every number between $13793$ and $10^{245}$ requires at most $16$.
Koichi Kawada, Trevor Dion Wooley and Jean-Marc Deshouillers extended Harold Davenport's $1939$ result to show that every number above $10^{220}$ requires no more than $16$.
Sources
- 2000: Jean-Marc Deshouillers, François Hennecart and Bernard Landreau: Waring's Problem for Sixteen Biquadrates -- Numerical Results (Journal de théorie des nombres de Bordeaux Vol. 12: pp. 411 – 422)