  We show that deciding the equality of two Dedekind sums $S(c,b)$, $S(d,b)$ is
equivalent to deciding whether a Dedekind sum defined by $b, c, d$ takes a
certain value. By means of this result we construct infinite sequences of
pairwise equal Dedekind sums. Moreover, we prove a result that says how many
Dedekind sums $S(d,b)$, $1\le d\le b-1$, may be equal to a given $S(c,b)$ if
$b$ is a square-free number.
