The Solvability of Polynomial Pell’s Equation

  • Bal Bahadur Tamang Central Department of Mathematics, Tribhuvan University, Kirtipur, Kathmandu
  • Ajay Singh Department of Mathematics, M. R. M. Campus, Tribhuvan University, Ilam
Keywords: Continued fraction, Diophantine equation, Integers, Polynomial Pell’s equation

Abstract

This article attempts to describe the continued fraction expansion of ÖD viewed as a Laurent series x-1. As the behavior of the continued fraction expansion of ÖD is related to the solvability of the polynomial Pell’s equation p2-Dq2=1  where D=f2+2g  is monic quadratic polynomial with deg g<deg f  and the solutions p, q  must be integer polynomials. It gives a non-trivial solution if and only if the continued fraction expansion of ÖD  is periodic.

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Abstract
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Published
2020-12-25
How to Cite
Tamang, B., & Singh, A. (2020). The Solvability of Polynomial Pell’s Equation. Journal of Institute of Science and Technology, 25(2), 125-132. https://doi.org/10.3126/jist.v25i2.33749
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