Smallest Triple of Consecutive Sums of Squares

Theorem

The smallest triple of consecutive positive integers each of which is the sum of two squares is:

$\tuple {232, 233, 234}$

Proof

We have:

\(\ds 232\)

\(=\)

\(\ds 14^2 + 6^2\)

\(\ds 233\)

\(=\)

\(\ds 13^2 + 8^2\)

\(\ds 234\)

\(=\)

\(\ds 15^2 + 3^2\)

This theorem requires a proof. In particular: It remains to be shown this is the smallest such triple. 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): $232$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $232$