This nal project discusses the technique of the alternating sum properties by using congruence modulo 4. Analytically this technique is implemented for Dedekind sums mod Z, 2Z and 4Z. The equations then are combined with Barkan-Hickerson-Knuth's formula from the Dedekind sums being partitioned by using the concept the continued fraction expansion. Keywords: Dedekind sums, Barkan-Hickerson…