Question 127
Let $p, q$ be coprime integers, such that $\frac{p}{q} \le 1$. For which $p, q$, there exist even integers $b_1, b_2, \dots, b_n$, such that
$$
\frac{p}{q} = \frac{1}{b_1 + \frac{1}{b_2 + \frac{1}{b_3 + \dots}}}?
$$
$$
\frac{p}{q} = \frac{1}{b_1 + \frac{1}{b_2 + \frac{1}{b_3 + \dots}}}?
$$