A division algorithm approach to p-adic Sylvester expansions

doi:10.1016/j.jnt.2015.08.016

Journal of Number Theory

Volume 160, March 2016, Pages 1-10

https://doi.org/10.1016/j.jnt.2015.08.016 Get rights and content

Under an Elsevier user license

open archive

Abstract

A method of constructing finite p-adic Sylvester expansions for all rationals is presented. This method parallels the classical Fibonacci–Sylvester (greedy) algorithm by iterating a p-adic division algorithm. The method extends to irrational p-adics that have an embedding in the reals.

MSC

11A67

11J61

Keywords

p-Adic number

p-Adic division algorithm

Sylvester series expansion