  We propose that the stability of dark matter is ensured by a discrete
subgroup of the U(1)B-L gauge symmetry, Z_2(B-L). We introduce a set of chiral
fermions charged under the U(1)B-L in addition to the right-handed neutrinos,
and require the anomaly-cancellation conditions associated with the U(1)B-L
gauge symmetry. We find that the possible number of fermions and their charges
are tightly constrained, and that non-trivial solutions appear when at least
five additional chiral fermions are introduced. The Fermat theorem in the
number theory plays an important role in this argument. Focusing on one of the
solutions, we show that there is indeed a good candidate for dark matter, whose
stability is guaranteed by Z_2(B-L).
