= p-adic digit
{c}
{title2=$b_j\in\{0,\ldots,p-1\}$}
The <p-adic digits> are the unique coefficients in $x=\sum_{j\geq0}b_jp^j$ for a <p-adic integer> $x$. Taking least nonnegative representatives of its <congruence classes>,
$$
r_{n+1}=r_n+b_np^n,
$$
so each new residue determines one more <p-adic digit>. For $13$ in $\mathbb Z_2$, the low-to-high digits are $1,0,1,1,0,\ldots$, giving $13=1+0\cdot2+1\cdot4+1\cdot8$. A finite prefix describes a whole <coset>, not a unique infinite expansion.
Back to article page
