The p-adic numbers are an extension of the rational numbers first described by [Kurt Hensel]? in 1897. They have been used to solve several problems in number theory, many of them using [Helmut Hasse]?'s [local-global principle]?, which roughly states that an equation can be solved over the rational numbers if it can be solved over the real numbers and over the p-adic numbers for every prime numberp.
For every prime numberp, the p-adic numbers form an extension of the rational numbers first described by [Kurt Hensel]? in 1897. They have been used to solve several problems in number theory, many of them using [Helmut Hasse]?'s [local-global principle]?, which roughly states that an equation can be solved over the rational numbers if it can be solved over the real numbers and over the p-adic numbers for every prime p.
Changed: 3c3
If p is a prime number, then any integer can be written as a p-adic expansion in the form
If p is a fixed prime number, then any integer can be written as a p-adic expansion in the form
Changed: 33,34c33,34
We start with the [inverse limit]? of the abelian groups Zpn: a p-adic integer is then a sequence
![[Home]](wikipedia.png)