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Perfect powers in solutions to Pell equations
Potencias perfectas en soluciones a las ecuaciones de Pell
Palabras clave:
Pell equation, Diophantine application (en)Ecuación de Pell, Aplicación diofántica (es)
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Abstract. 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.
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.
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