Residue Field of P-adic Norm on Rationals

Theorem
Let $\norm {\,\cdot\,}_p$ be the $p$-adic norm on the rationals $\Q$ for some prime $p$.

The induced residue field on $\struct {\Q,\norm {\,\cdot\,}_p}$ is the Galois field $\F_p$ with $p$ elements.