SOLUCIONES RACIONALES DE LA ECUACIÓN XY = YX

Jorge E. Hernández; Edith C. de Hernández

Submitted September 6, 2019

Published 2011-06-01

Artículos

Vol. 13 No. 1 (2011): Tecnociencia

SOLUCIONES RACIONALES DE LA ECUACIÓN XY = YX

Jorge E. Hernández⁺⁻
Edith C. de Hernández⁺⁻

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Citación:

DOI: ND

Published: 2011-06-01

How to Cite

E. Hernández, J. and de Hernández, E. C. (2011) “SOLUCIONES RACIONALES DE LA ECUACIÓN XY = YX”, Tecnociencia, 13(1), pp. 129–140. Available at: https://revistas.up.ac.pa/index.php/tecnociencia/article/view/924 (Accessed: 18 August 2024).

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Abstract

In this paper we study the diophantine equation mn = nm with m ? n, proving that the only integer solutions of this equation are (2, 4) and (4, 2). Then we determine the shape of all the rational solutions of the equation xy = yx with x ?y, and prove that these solutions are unique. We also present the intervals where are the positive rational solutions of the equation xy = yx