Positive rational solutions to $x^y = y^{mx}$: a number-theoretic excursion

Details Positive rational solutions to $x^y = y^{mx}$: a number-theoretic excursion Positive rational solutions to $x^y = y^{mx}$: a number-theoretic excursion

2002-09-06

arxiv.org/abs/math/0209072v1

Mathematics

Number Theory

12 pages

Scientific paper

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.

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