Let $a \in \Bbb{N}$ and let $d$ be a positive real number with a continued fraction expansion of $[0;\overline{1,a,1}]$.
Prove for all $t \gt 2$ the following inequality does not have infinitely many solutions:
$$\left| d - \frac{p}{q} \right| \lt \frac{1}{q^t}$$
Then, in particular, prove if $a=2$:
$$\left| d - \frac{p}{q} \right| \gt \frac{1}{14q^2}$$
I have no idea where to begin in solving these problems, any help would be appreciated.