Largest Number not Expressible as Sum of Less than 32 Positive Fifth Powers

Theorem

The largest positive integer which cannot be expressed as the sum of less than $32$ positive fifth powers is $466$:

$466 = 18 \times 1^5 + 14 \times 2^5$

Proof

This theorem requires a proof. In particular: It needs to be shown that there are no larger numbers with this property. 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.

Also see

• Hilbert-Waring Theorem

Sources

• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $466$