{"title":"On the Integer Solutions of the Pell Equation x2 - dy2 = 2t","authors":"Ahmet Tekcan, Bet\u00fcl Gezer, Osman Bizim","volume":1,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":104,"pagesEnd":109,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/423","abstract":"

Let k ≥ 1 and t ≥ 0 be two integers and let d = k2 + k be a positive non-square integer. In this paper, we consider the integer solutions of Pell equation x2 - dy2 = 2t. Further we derive a recurrence relation on the solutions of this equation.<\/p>\r\n","references":" Arya S.P. On the Brahmagupta-Bhaskara Equation. Math. Ed. 8(1)(1991), 23-27. Baltus C. Continued Fractions and the Pell Equations:The work of Eulerand Lagrange. Comm. Anal. Theory Contin. Fractions 3(1994), 4-31. Barbeau E. Pell's Equation. Springer Verlag, 2003. Edwards, H.M. Fermat's Last Theorem. A Genetic Introduction to Alge-braic Number Theory. Corrected reprint of the 1977 original. GraduateTexts in Mathematics, 50. Springer-Verlag, New York, 1996. Kaplan P. and Williams K.S. Pell's Equations x2-my2 = -1,-4 and Continued Fractions. Journal of Number Theory 23(1986), 169-182. Koblitz N. A Course in Number Theory and Cryptography. Graduate Texts in Mathematics, Second Edition, Springer, 1994. Lenstra H.W. Solving The Pell Equation. Notices of the AMS 49(2)(2002), 182-192. Matthews, K. The Diophantine Equation x2-Dy2 = N, D > 0. Expo-sitiones Math.18 (2000), 323-331. Mollin R.A., Poorten A.J. and Williams H.C. Halfway to a Solution ofx2 - Dy2 = ?3. Journal de Theorie des Nombres Bordeaux, 6(1994),421-457. Niven I., Zuckerman H.S. and Montgomery H.L. An Introduction to the Theory of Numbers. Fifth Edition, John Wiley&Sons, Inc., New York,1991. Stevenhagen P. A Density Conjecture for the Negative Pell Equation.Computational Algebra and Number Theory, Math. Appl. 325 (1992),187-200. Tekcan A. Pell Equation x2 - Dy2 = 2, II. Bulletin of the Irish Mathematical Society 54 (2004), 73?89. Tekcan A., Bizim O. and Bayraktar M. Solving the Pell Equation Using the Fundamental Element of the Field Q(\u00d4\u00ea\u00dc\u0394). South East Asian Bull.of Maths. 30(2006), 355-366. Tekcan A. The Pell Equation x2 -Dy2 = \u252c\u25924. Appl. Math. Sci., 1(8)(2007), 363-369.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 1, 2007"}