Positive rational solutions to xy = ymx: a number-theoretic excursion
Michael A. Bennett, Bruce Reznick
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.
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