{"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":"<p>Let k &ge; 1 and t &ge; 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":"[1] Arya S.P. On the Brahmagupta-Bhaskara Equation. Math. Ed. 8(1)(1991), 23-27.[2] Baltus C. Continued Fractions and the Pell Equations:The work of Eulerand Lagrange. Comm. Anal. Theory Contin. Fractions 3(1994), 4-31.[3] Barbeau E. Pell's Equation. Springer Verlag, 2003.[4] 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.[5] Kaplan P. and Williams K.S. Pell's Equations x2-my2 = -1,-4 and Continued Fractions. Journal of Number Theory 23(1986), 169-182.[6] Koblitz N. A Course in Number Theory and Cryptography. Graduate Texts in Mathematics, Second Edition, Springer, 1994.[7] Lenstra H.W. Solving The Pell Equation. Notices of the AMS 49(2)(2002), 182-192.[8] Matthews, K. The Diophantine Equation x2-Dy2 = N, D > 0. Expo-sitiones Math.18 (2000), 323-331.[9] 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.[10] 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.[11] Stevenhagen P. A Density Conjecture for the Negative Pell Equation.Computational Algebra and Number Theory, Math. Appl. 325 (1992),187-200.[12] Tekcan A. Pell Equation x2 - Dy2 = 2, II. Bulletin of the Irish Mathematical Society 54 (2004), 73?89.[13] 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.[14] 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"}