Question #198667

Define p-adic number with example.


1
Expert's answer
2021-06-01T13:09:24-0400

Every natural number m defines a sequence:

anm(mod pn)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,...)(1,3,3,3,3,35,35,35,...)

a1=35(mod 2)=1a_1=35(mod\ 2)=1

a2=35(mod 22)=3a_2=35(mod\ 2^2)=3

a2=35(mod 23)=3a_2=35(mod\ 2^3)=3

etc.


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