Solving higher-order p-adic polynomial equations via newton-raphson method

We consider the root-finding problem f (x) = 0,f ∈ zp[x],and seek a root in zp of this equation through a p-adic analogue of newton-raphson method. we show in particular that,under appropriate assumptions,the sequence of approximants generated by the iterative formula of the newton-raphson method converges to a unique root of f in zp. also,we give the rate of convergence of this method in the p-adic setting. our work generalizes previous results concerning q-th roots of p-adic numbers due to kecies and zerzaihi (2013) and ignacio et al. (2016).