intros n m; elim m.
rewrite Zpower_nat_1; simpl in |- *; auto with zarith.
intros n0 H H0; replace (S (S n0)) with (1 + S n0); auto with arith.
rewrite Zpower_nat_is_exp; rewrite Zpower_nat_1; simpl in |- *;
auto with zarith.
Qed.

Theorem OddExp :
forall (n : Z) (m : nat), Odd n -> Odd (Zpower_nat n m).