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:

$\ds 232$

$=$

$\ds 14^2 + 6^2$

$\ds 233$

$=$

$\ds 13^2 + 8^2$

$\ds 234$

$=$

$\ds 15^2 + 3^2$

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In particular: It remains to be shown this is the smallest such triple.
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Sources

1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $232$
1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $232$