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

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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.
12 pages

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Number Theory, 11D41

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http://salesiana.dossiersoluciones.com/handle/123456789/64875

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0209072
 http://arxiv.org/abs/math/0209072

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arXiv