p-adic integer

《Algebraic Number Theory》 · 第 100 页 · Chapter II，Section 1「The p-adic Numbers」，Definition 1.1

Fix a prime number $p$. A $p$-adic integer is a formal infinite series $a_0+a_1p+a_2p^2+\cdots$, where $0\leq a_i<p$, for all $i=0,1,2,\ldots$. The set of all $p$-adic integers is denoted by $\mathbb Z_p$.