User:Leigh.Samphier/Sandbox/Canonical P-adic Expansion of Rational is Eventually Periodic

Theorem
Let $\struct {\Q_p, \norm {\,\cdot\,}_p}$ be the $p$-adic numbers for some prime $p$.

Let $x \in \Q_p$.

Then:
 * $x$ is a rational number the canonical expansion of $x$ is eventually periodic

Necessary Condition
Let $x$ be a rational number.