A 
-adic integer is a p-adic number of the form 
, where 
, 
are integers, and 
is prime. It is sufficient to take 
in the set 
.
Equivalently, a 
-adic integer is an element of the inverse limit of the rings 
for 
.
The same ring is obtained by taking the 
to be any rationals with denominator coprime to 
.
