intros v p; elim p.
unfold maxDiv in |- *; rewrite Zpower_nat_O; auto.
apply Zdivides1.
simpl in |- *.
intros n H'; case (ZdividesP v (radix * Zpower_nat radix n)); simpl in |- *;
auto with zarith.
Qed.

Theorem maxDivSimplAux :
forall (v : Z) (p q : nat),
p = maxDiv v (S (q + p)) -> p = maxDiv v (S p).