OLVER’S METHOD FOR SOLVING ROOTS OF p-ADIC POLYNOMIAL EQUATIONS

Abstract

Let \(\mathbb{Z}\)_p[x] be the set of all functions whose coefficients are in the field of p-adic integers \(\mathbb{Z}\)_p.  This work considers a problem of finding a root of a polynomial equation P(x) = 0 where P(x) ∈ \(\mathbb{Z}\)_p[x].  The solution is approximated through an analogue of Olver’s method for finding roots of polynomial equations P(x) = 0 in \(\mathbb{Z}\)_p.