Continued Fraction Expansion of Irrational Square Root

Theorem
Let $n \in \Z$ such that $n$ is not a square.

Then the continued fraction expansion of $\sqrt n$ is of the form:
 * $\left[{a_1 \left \langle{b_1, b_2, \ldots, b_{m-1}, b_m, b_{m-1}, \ldots, b_2, b_1, 2 a_1}\right \rangle}\right]$

or
 * $\left[{a_1 \left \langle{b_1, b_2, \ldots, b_{m-1}, b_m, b_m, b_{m-1}, \ldots, b_2, b_1, 2 a_1}\right \rangle}\right]$

where $m \in \Z: m \ge 0$.

That is, it has the form as follows:
 * It is periodic;
 * It starts with an integer $a_1$;
 * Its cycle starts with a palindromic bit $b_1, b_2, \ldots, b_{m-1}, b_m, b_{m-1}, \ldots, b_2, b_1$ or $b_1, b_2, \ldots, b_{m-1}, b_m, b_m, b_{m-1}, \ldots, b_2, b_1$ which may be of length zero;
 * Its cycle ends with twice the first partial quotient.