Continued Fractions with Partial Quotients Bounded in Average
Joshua N. Cooper
Abstract
We ask, for which n does there exists a k, 1 ≤ k < n and (k,n)=1, so that k/n has a continued fraction whose partial quotients are bounded in average by a constant B? This question is intimately connected with several other well-known problems, and we provide a lower bound in the case of B=2.
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