Concept

Summary
In number theory, given a prime number p, the p-adic numbers form an extension of the rational numbers which is distinct from the real numbers, though with some similar properties; p-adic numbers can be written in a form similar to (possibly infinite) decimals, but with digits based on a prime number p rather than ten, and extending (possibly infinitely) to the left rather than to the right. Formally, given a prime number p, a p-adic number can be defined as a series :s=\sum_{i=k}^\infty a_i p^i = a_k p^k + a_{k+1} p^{k+1} + a_{k+2} p^{k+2} + \cdots where k is an integer (possibly negative), and each a_i is a integer such that 0\le a_i < p. A p-adic integer is a p-adic number such that k\ge 0. In general the series that represents a p-adic number is not convergent in the usual sense, but it is convergent
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