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The sum of all partial quotients in the regular continued fraction expansions of m/n, for 1 ≤ m ≤ n, is shown to be 6π-2n(ln n)2 + O(n log n(log log n)2). This result is applied to the analysis of what is perhaps the oldest non-trivial algorithm for number-theoretic computations.
Keywords: continued fractions, partial quotients, number theory
