ON THE EXISTENCE OF p-ADIC ROOTS

Abstract

Abstract. In this paper, we give the condition for the existence of the q-th roots of p-adic numbers in Q p with an integer q ≥ 2 and (p, q) = 1. We have the conditions for the existence of the fifth root and the seventh root of p-adic numbers in Q p , respectively.

NEWTON-RAPHSON METHOD FOR COMPUTING p-ADIC ROOTS

“…The following theorem provides the conditions for the existence of the q-th roots of p-adic numbers ( [6]). Theorem 2.5.…”