¹Harish-Chandra Research Institute, Allahabad, India. Email: kalyan@mri.ernet.in
²UNAM, Morelia, Mexico. Email: fluca@matmor.unam.mx

In this paper, we study the appearance of perfect powers in the first component of a non-minimal solution of a Pell equation. We give an upper bound on the counting function of the positive integers n having the property that some power of it (of exponent larger than 1) is the first component of a non-minimal solution of a Pell equation, and we present a Diophantine application.

Key words: Pell equation.

En este trabajo, investigamos la aparición de las potencias perfectas en la primera componente de una solución no minimal de una ecuación de Pell. Damos una cota superior sobre la función de conteo del conjunto de los enteros positivos n tal que alguna potencia suya con exponente mayor que 1 es la primera componente de una solución no-minimal de una ecuación de Pell y presentamos una aplicación Diofántica.

Palabras clave: Ecuación de Pell.

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