A strengthening of a theorem of Bourgain and Kontorovich. III

摘要

We prove that the set of positive integers contains a positive proportion of denominators of the finite continued fractions all of whose partial quotients belong to the alphabet {1, 2, 3, 4, 10}. The corresponding theorem was previousy known only for the alphabet {1, 2, 3, 4, 5} and for alphabets of larger cardinality.