# Hilbert-Waring Theorem/Variant Form/Particular Cases/3/Historical Note

< Hilbert-Waring Theorem | Variant Form | Particular Cases | 3

Jump to navigation
Jump to search
## Particular Case of the Hilbert-Waring Theorem -- Variant Form: $k = 3$: Historical Note

It had been established by $1912$ that it takes no more than $9$ positive cubes to represent any positive integer as a sum.

The value of $G \left({3}\right)$ is still the subject of research.

Yuri Vladimirovich Linnik showed in $1943$ that the upper bound of $G \left({3}\right)$ is $7$.

Recent research, however, suggests that $G \left({3}\right)$ may indeed be $4$.