revert i j; induction v; intros i j Hi.
+ cbn; intros ? % divides_1_inv % not_qs_1; auto.
+ cbn; intros [ H % divides_pow | H  ] % divides_mult_inv; eauto.
* eapply primestream_divides in H; omega.
* eapply IHv in H; eauto.
Qed.

Lemma qs_shift n m j k (v : vec nat k) :
divides (qs n) (exp j v) <-> divides (qs (m + n)) (exp (m + j) v).