English

A counting method for finding rational approximates to arbitrary order roots of integers

General Mathematics 2007-05-23 v1

Abstract

It is shown that for finding rational approximates to m'th root of any integer to any accuracy one only needs the ability to count and to distinguish between m different classes of objects. To every integer N can be associated a 'replacement rule' that generates a word W* from another word W consisting of symbols belonging to a finite 'alphabet' of size m. This rule applied iteratively on almost any initial word W0, yields a sequence of words {Wi} such that the relative frequency of different symbols in the word Wi approaches powers of the m'th root of N as i tends to infinity

Keywords

Cite

@article{arxiv.math/9912090,
  title  = {A counting method for finding rational approximates to arbitrary order roots of integers},
  author = {Ashok Kumar Gupta and Ashok Kumar Mittal},
  journal= {arXiv preprint arXiv:math/9912090},
  year   = {2007}
}
R2 v1 2026-07-22T18:05:44.788Z