p-adic number

Summary

For a prime number $p$, the $p$-adic numbers form the field $\Q_p$, the completion of $\Q$ for the p-adic absolute value. In $\Q_p$, a number is small when it is divisible by a high power of $p$. The field $\Q_p$ is a local field of characteristic $0$. Questions about congruences modulo all powers of $p$ become questions about equations in $\Q_p$.