Hilbert-Waring Theorem/Particular Cases/3/Historical Note

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Particular Case of the Hilbert-Waring Theorem: $k = 3$: Historical Note

Edward Waring knew that some integers required at least $9$ positive cubes to represent them as a sum:

\(\displaystyle 23\) \(=\) \(\displaystyle 2^3 + 2^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3\)
\(\displaystyle 239\) \(=\) \(\displaystyle 4^3 + 4^3 + 3^3 + 3^3 + 3^3 + 3^3 + 1^3 + 1^3 + 1^3\)

The fact that $\map g 3 = 9$ was established from $1909$ to $1912$ by Arthur Josef Alwin Wieferich and Aubrey John Kempner.


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