Hilbert-Waring Theorem/Particular Cases/6

Particular Case of the Hilbert-Waring Theorem: $k = 6$

The Hilbert-Waring Theorem states that:

For each $k \in \Z: k \ge 2$, there exists a positive integer $\map g k$ such that every positive integer can be expressed as a sum of at most $\map g k$ $k$th powers.

The case where $k = 6$ is:

Every positive integer can be expressed as the sum of at most $73$ positive sixth powers.

That is:

$\map g 6 = 73$

Proof

This theorem requires a proof. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{ProofWanted}} from the code. If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $73$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $73$