Abstract

Solving Pell’s Equation via Lattice Reduction

P. Anuradha Kameswari* and S B T Sundari Katakam

Department of Mathematics, Andhra University, Visakhapatnam - 530003, Andhra Pradesh, INDIA.

ABSTRACT

In this paper, we adapted rational approximation of for a non square positive integer via lattice reduction of a quadratic form for , decimal approximation of to the precision , we obtained the convergent of that is a solution of Pell’s equation as a short vector of the above quadratic form for an appropriate .

Keywords :Pell’s equation, convergent, Lattice reduction, LLL algorithm, quadratic form.

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