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

Some answers from Applications of finite continued fractions in fact are Applications of periodic continued fractions. I think that it should be separate question. What can you add to the following ...

I know some applications of finite continued fractions. Probably you know more. Can you add anything? (For Applications of periodic continued fractions I have made a special topic.) 1) (Trivial) ...