Generating Infinitely Many Satisfactory Colorings of Positive Integers

Authors

Lon Mitchell, University of South Florida St. PetersburgFollow

SelectedWorks Author Profiles:

Lon Mitchell

Document Type

Article

Publication Date

2019

ISSN

0012-365X

Abstract

An n-satisfactory coloring of then-smooth integers is an assignment of n colors to the positive integers whose prime factors are at most n so that for each such m, the integers m, 2m,..., nm receive different colors. In this note, we give a short proof that infinitely many 6-satisfactory colorings of the 6-smooth integers exist and show how the technique of the proof can be applied more generally, including for n ∈ {8,10,12}.

Publisher

Elsevier

Recommended Citation

Mitchell, L. (2019). Generating infinitely many satisfactory colorings of positive integers. Discrete Mathematics, 342(12). https://doi.org/10.1016/j.disc.2019.111602.