P Adic Numbers An Introduction

P Adic Numbers An Introduction

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a p adic number is an extension of the field of rationals such that congruences modulo powers of a fixed prime p are related to proximity in the so called p adic metric any nonzero rational number x can be represented by xpar s 1 where p is a prime number r and s are integers not divisible by p and a is a unique integer then define the p adic norm of x by x pp a