Congruences modulo 4 for the alternating sum of the partial quotients

摘要

We apply a technique used in [E. Tsukerman, Equality of Dedekind sums mod Z, 2Z and 4Z, Int. J. Number Theory 11(6) (2015) 1735-1738] combined with the Barkan-Hickerson-Knuth formula in order to obtain congruences modulo 4 for the alternating sum of the partial quotients of the continued fraction expansion of a/b, where 0 < a < b are integers.