table of continued fractions of $\sqrt{n}$ for $1 < n < 102$

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Major Section:
Reference
Type of Math Object:
Data Structure
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Mathematics Subject Classification

11A25 no label found

Comments

"End" of periodic part of continued fractions of square root...

"As the table shows, the periodic part ends with $2 \lfloor \sqrt{n} \rfloor$."

Interesting. So the continued fraction of sqrt(n^2 + 1) is always of the form n; 2n. Why is this?