2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/99895We ask, for which $n$ does there exists a $k$, $1 \leq k < n$ 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=2.7 pages, 0 figures; minor changes, to appear in Fibonacci QuarterlyNumber TheoryCombinatorics11K50; 11K38text