Problem:
If $x = \frac{15529}{17676}$, then find $\frac{1}{x+\frac{1}{x+\frac{1}{x+\ddots}}}$.
Answer:
$\frac{\sqrt{1490913745}-15529}{35352}$
{'source': 'AMPS', 'file': 'amps/mathematica/number_theory/continued_fraction/44749.txt'}