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 $a = 1$.

$\blacksquare$

Sources

• 1965: J.A. Green: Sets and Groups ... (previous) ... (next): $\S 2.6$. Algebra of congruences: Example $42 \ (4)$