Equality of Dedekind sums modulo 8Z by

1. Background. Dedekind sums are classical objects of study intro-duced by Richard Dedekind in the 19th century in his study of the η-function [Ded53]. Among many other areas of mathematics, Dedekind sums appear in: geometry (lattice point enumeration in polytopes [BR07]), topology (sig-nature defects of manifolds [HZ74]) and algorithmic complexity (pseudo-random number generators [Knu98]). To define the Dedekind sums, let ((x)) = x − bxc − 1/2 if x ∈ R \ Z, 0 if x ∈ Z. Then the Dedekind sum s(a, b) for a, b ∈ N coprime is defined by s(a, b) = b∑ k=1 a