Hilbert-Waring Theorem/Variant Form/Historical Note

Historical Note on Waring's Problem

The Hilbert-Waring Theorem was conjectured by Edward Waring in $1770$ in Meditationes Algebraicae, and was generally referred to as Waring's problem.

It was proved by David Hilbert in $1909$.

Its variant form was investigated by Godfrey Harold Hardy and John Edensor Littlewood.

The assertion is that for each $k$ there exist such a number $G \left({k}\right)$.

The problem remains to determine what that $G \left({k}\right)$ actually is.