On Polynomials Solutions of Quadratic Diophantine Equations
Amara Chandoul
DOI: 10.4236/apm.2011.14028   PDF    HTML     5,463 Downloads   11,136 Views   Citations


Let P:=P(t) be a polynomial in Z[X]\{0,1} In this paper, we consider the number of polynomial solutions of Diophantine equation E:X2–(P2P)Y2–(4P2–2)X+(4P2–4P)Y=0. We also obtain some formulas and recurrence relations on the polynomial solution (Xn,Yn) of E

Share and Cite:

A. Chandoul, "On Polynomials Solutions of Quadratic Diophantine Equations," Advances in Pure Mathematics, Vol. 1 No. 4, 2011, pp. 155-159. doi: 10.4236/apm.2011.14028.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] I. Niven, H. S. Zuckerman and H. L. Montgomery, “An Introduction to the Theory of Numbers,” 5th Edition, Ox-ford University Press, Oxford, 1991.
[2] A. Tekcan, “The Pell Equation ,” Applied Mathematical Sciences, Vol. 1, No. 8, 2007, pp. 363-369.
[3] P. Kaplan and K. S Williams, “Pell’s Equation and Continued Fractions,” Journal of Num-ber Theory, Vol. 23, No. 2, 1986, pp. 169-182. doi:10.1016/0022-314X(86)90087-9
[4] K. Matthews, “The Diophantine Equation ,” Expositiones Mathematicae, Vol. 18, 2000, pp. 323-331.
[5] R. A. Mollin, A. J Poorten and H. C. Williams, “Halfway to a Solution of ,” Journal de Theorie des Nombres Bordeaux, Vol. 6, No. 2, 1994, pp. 421-457.
[6] P. Stevenhagen, “A Density Conjecture for the Negative Pell Equation, Computational Algebra and Number Theory,” Math. Appl. Vol. 325, 1992, pp. 187-200.
[7] A. Chandoul, “The Pell Equation ,” Research Journal of Pure Algebra, Vol. 1, No. 2, 2011, pp. 11-15.
[8] A. S. Shabani, “The Proof of Two Conjectures Related to Pell’s Equation ,” International Journal of Computational and Mathematical Sciences, Vol. 2, No. 1, 2008, pp. 24-27.
[9] A. Chandoul, “The Pell Equation ,” Advances in Pure Mathematics, Vol. 1, No. 2, 2011, pp. 16-22. doi:10.4236/apm.2011.12005
[10] A. Dubickas and J. Steuding, “The Polynomial Pell Equation,” Elemente der Mathematik, Vol. 59, No. 4, 2004, pp. 133-143. doi:10.1007/s00017-004-0214-7
[11] A. Tekcan, “Quadratic Diophantine Equation , Bulletin of Malay-sian Mathematical Society, Vol. 33, No. 2, 2010, pp. 273-280.
[12] A. Chandoul, “On Quadratic Diophantine Equation ,” International Mathematical Forum, Vol. 6, No. 36, 2011, pp. 1777-1782.

Copyright © 2024 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.