I propose to collect here open problems from the theory of continued fractions. Any types of continued fractions are welcome.



Open problems in continued fractions theory
Guy, Unsolved Problems In Number Theory, F21, attributes to Bohuslav Divis the conjecture that in each real quadratic field there is an irrational with all partial quotients 1 or 2; more generally, same question but with 1 and 2 replaced by any pair of distinct positive integers. 


