The Pell Equation X2 - Dy2 = ± k2

DOI: 10.4236/apm.2011.12005   PDF   HTML     6,028 Downloads   15,825 Views   Citations


Let D≠1 be a positive non-square integer and k≥2 be any fixed integer. Extending the work of A. Tek-can, here we obtain some formulas for the integer solutions of the Pell equation X2 - Dy2 = ± k2 .

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A. Chandoul, "The Pell Equation X2 - Dy2 = ± k2," Advances in Pure Mathematics, Vol. 1 No. 2, 2011, pp. 16-22. doi: 10.4236/apm.2011.12005.

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The authors declare no conflicts of interest.


[1] A. Tekcan, “The Pell Equation ,” Applied Mathematical Sciences, Vol. 1, No. 8, 2007, pp. 363-369.
[2] P. Kaplan and K. S. Williams, “Pell’s Equation and continued fractions,” Journal of Num-ber Theory, Vol. 23, 1986, pp. 169-182.
[3] K. Matthews, “The Diophantine Equation ,” Expositiones Mathematicae, Vol. 18, 2000, pp. 323-331. doi:10.1016/0022-314X(86)90087-9
[4] R. A. Mollin, A. J. Poorten and H. C. Williams, “Halfway to a Solution of ,” Journal de Theorie des Nombres Bordeaux, Vol. 6, 1994, pp. 421-457.
[5] P. Stevenhagen, “A Density Conjecture for the negative Pell Equation, Computational Al-gebra and Number Theory,” Mathematics and its Applications, Vol. 325, 1995, 187-200.
[6] 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.
[7] I. Niven, H. S. Zuckerman and H. L. Montgomery, “An Introduction to the Theory of Numbers,” 5th Edition, Wiley, the Republic of Sin-gapore, 1991.

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