Positive rational solutions to $x^y = y^{mx}$: a number-theoretic excursion
Number Theory
2007-05-23 v1
Abstract
We give a light-hearted look at the topic in the title. Most solutions are in semi-boring parametric families, but some are sporadic and come from Thue equations. One amusing example is m = 2, x = (4/5)^128, y = (4/5)^125.
Cite
@article{arxiv.math/0209072,
title = {Positive rational solutions to $x^y = y^{mx}$: a number-theoretic excursion},
author = {Michael A. Bennett and Bruce Reznick},
journal= {arXiv preprint arXiv:math/0209072},
year = {2007}
}
Comments
12 pages