Odd Numbers Not Expressible as Sum of 5 Distinct Non-Zero Coprime Squares

Theorem

The largest odd positive integer that cannot be expressed as the sum of exactly $5$ non-zero square numbers all of which are coprime is $245$.

This article is complete as far as it goes, but it could do with expansion. In particular: The full list of those numbers is to be investigated. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by adding this information. 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 {{Expand}} from the code. If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.

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

• 1994: Paul T. Bateman, Adolf J. Hildebrand and George B. Purdy: Sums of Distinct Squares (Acta Arith. Vol. 67, no. 4: pp. 349 – 380)

• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $157$