  For $a\in \Bbb Z$ and $b\in\Bbb N$, $(a,b)=1$, let $s(a,b)$ denote the
classical Dedekind sum. We show that Dedekind sums take this value infinitely
many times in the following sense. There are pairs $(a_i,b_i)$, $i\in\Bbb N$,
with $b_i$ tending to infinity as $i$ grows, such that $s(a_i,b_i)=s(a,b)$ for
all $i\in \Bbb N$.
