This paper describes digit-by-digit integer restoring and non-restoring algorithms for
computing the cube root of a 33-bit radicand and gives improved methods for the …

This work offers an analogue of Householder's Method for solving a root-finding problem\(f
(x)= 0\) in the\(p\)-adic setting. We apply this method to calculate the square roots of a\(p\) …

This work offers an analogue of Halley's method for solving a rootfinding problem f (x)= 0 in
the p-adic setting. In particular, a root of the general polynomial equation f (x)= a0+ a1x+ …

Hensel's lemma is an important result in valuation theory which gives information on finding
roots of polynomials. A classical application of this result deals with the problem of finding …

Let Zp [x] be the set of all functions whose coefficients are in the field of p-adic integers Zp.
This work considers a problem of finding a root of a polynomial equation P (x)= 0 where P …

The study of the field of $ p $-adic numbers has been an important area of research in
mathematics, giving rise to several important results such as the Hasse-Minkowski Theorem …

Hensel's lemma has been the basis for the computation of the square roots of p-adic
numbers in Zp. We generalize this problem to the computation of qth roots of p-adic numbers …

Dans ce travail nous nous intéressons au calcul des racines carrées des nombres p-
adiques, en utilisant la méthode de Householder et ceci à travers le calcul de la solution …

In this paper, we compute the square roots of\(p\)-adic numbers in\(\mathbb {Q} _ {p}\), using
the secant method. We also study the performance of this method: the speed of its …

We consider Newton's method to compute the fifth root of a p-adic number in Qp. We have
the sufficient conditions for the convergence of Newton's method and the speed of its …