Prime Power of Sum Modulo Prime/Corollary

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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 $a = 1$.

$\blacksquare$


Sources