p-adic integer

Summary

The $p$-adic integers are the p-adic numbers $x$ with $\abs{x}_p \le 1$. They form a ring $\Z_p$, which is a discrete valuation ring with maximal ideal $p\Z_p$ and residue field $\F_p$. The ring $\Z_p$ is compact, and it is the inverse limit of the rings $\Z / p^n \Z$. It holds, in one object, the information of all congruences modulo powers of $p$.