Define p-adic number with example.
Every natural number m defines a sequence:
an≡m(mod pn)a_n\equiv m(mod\ p^n)an≡m(mod pn) , 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,...)(1,3,3,3,3,35,35,35,...)
a1=35(mod 2)=1a_1=35(mod\ 2)=1a1=35(mod 2)=1
a2=35(mod 22)=3a_2=35(mod\ 2^2)=3a2=35(mod 22)=3
a2=35(mod 23)=3a_2=35(mod\ 2^3)=3a2=35(mod 23)=3
etc.
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