A p-adic integer is a p-adic number of the form sum_(k = m)^∞ a_k p^k, where m>=0, a_k are integers, and p is prime. It is sufficient to take a_k in the set {0, 1, ..., p - 1}. Equivalently, a p-adic integer is an element of the inverse limit of the rings Z/p^k Z for k>=0. The same ring is obtained by taking the a_k to be any rationals with denominator coprime to p.
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