Abstract

CHAKRABORTY, KALYAN  and  LUCA, FLORIAN. Perfect powers in solutions to Pell equations. Rev.colomb.mat. [online]. 2009, vol.43, n.1, pp.71-86. ISSN 0034-7426.

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.

Keywords : Pell equation.

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