Answer to Question #198667 in Functional Analysis for smi

Question

Define p-adic number with example.

Answer 1

Every natural number m defines a sequence:

$a_n\equiv m(mod\ p^n)$ , p is a prime number

and can therefore be regarded as a p-adic integer.

For example, 35 as a 2-adic integer would be written as the sequence

$(1,3,3,3,3,35,35,35,...)$

$a_1=35(mod\ 2)=1$

$a_2=35(mod\ 2^2)=3$

$a_2=35(mod\ 2^3)=3$

etc.