  Lech proved in 1953 that the set of zeroes of a linear recurrence sequence in
a field of characteristic 0 is the union of a finite set and finitely many
infinite arithmetic progressions. This result is known as the
Skolem-Mahler-Lech theorem. Lech gave a counterexample to a similar statement
in positive characteristic. We will present some more pathological examples. We
will state and prove a correct analog of the Skolem-Mahler-Lech theorem in
positive characteristic. The zeroes of a recurrence sequence in positive
characteristic can be described using finite automata.
