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p-adic Integer


A p-adic integer is a p-adic number of the form sum_(k=m)^(infty)a_kp^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^kZ for k>=0.

The same ring is obtained by taking the a_k to be any rationals with denominator coprime to p.


See also

Inverse Limit, p-adic Norm, p-adic Number

Portions of this entry contributed by David Terr

Portions of this entry contributed by Helena Verrill

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References

Cassels, J. W. S. Ch. 2 in Lectures on Elliptic Curves. New York: Cambridge University Press, 1991.

Referenced on Wolfram|Alpha

p-adic Integer

Cite this as:

Terr, David; Verrill, Helena; and Weisstein, Eric W. "p-adic Integer." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/p-adicInteger.html

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