On Permutiples Having a Fixed Set of Digits
Abstract
A permutiple is the product of a digit preserving multiplication, that is, a number which is an integer multiple of some permutation of its digits. Certain permutiple problems, particularly transposable, cyclic, and, more recently, palintiple numbers, have been well-studied. In this paper we study the problem of general digit preserving multiplication. We show how the digits and carries of a permutiple are related and utilize these relationships to develop methods for finding new permutiple examples from old. In particular, we shall focus on the problem of finding new permutiples from a known example having the same set of digits.
Keywords
Cite
@article{arxiv.1511.02033,
title = {On Permutiples Having a Fixed Set of Digits},
author = {Benjamin V. Holt},
journal= {arXiv preprint arXiv:1511.02033},
year = {2017}
}
Comments
The new version includes an additional example which further illustrates how to use the results in the paper. Some details of certain calculations have also been added to make the paper easier to read. Also, some of the results have been condensed to streamline exposition and flow. Revised manuscript submitted to INTEGERS Electronic Journal of Combinatorial Number Theory on January 27th, 2017