Notation m := (b_nat*q-q*q-1)%nat.Notation Zm_ring := (Zp_is_ring Hm).Notation qz := (Z.of_nat q).Notation scal := (M22scal (Zp_mult Hm)).

Theorem expo_congruence n : (0 < n)%nat -> nat2Zp Hm (q * alpha_nat n) = nat2Zp Hm (alpha_nat (n-1) + power n q).