Prime Power of Sum Modulo Prime/Corollary

Corollary to Prime Power of Sum Modulo Prime
Let $p$ be a prime number.

Then:
 * $\forall n \in \N_{> 0}: \paren {1 + b}^{p^n} \equiv 1 + b^{p^n} \pmod p$

Proof
Follows immediately from Prime Power of Sum Modulo Prime by putting $a = 1$.