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  • Cited by 4
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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Nesterenko, A. Yu. 2009. Determination of integer solutions of a system of simultaneous Pell equations. Mathematical Notes, Vol. 86, Issue. 3-4, p. 556.


    Нестеренко, Алексей Юрьевич and Nesterenko, Alexey Yur'evich 2009. Нахождение целочисленных решений системы связанных уравнений Пелля. Математические заметки, Vol. 86, Issue. 4, p. 588.


    JADRIJEVIĆ, BORKA and ZIEGLER, VOLKER 2006. A SYSTEM OF RELATIVE PELLIAN EQUATIONS AND A RELATED FAMILY OF RELATIVE THUE EQUATIONS. International Journal of Number Theory, Vol. 02, Issue. 04, p. 569.


    Bennett, Michael A 1997. Solving Families of Simultaneous Pell Equations. Journal of Number Theory, Vol. 67, Issue. 2, p. 246.


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  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 103, Issue 1
  • January 1988, pp. 35-46

Simultaneous Pellian equations

  • R. G. E. Pinch (a1)
  • DOI: http://dx.doi.org/10.1017/S0305004100064598
  • Published online: 24 October 2008
Abstract

In this paper we describe a method for finding integer solutions of simultaneous Pellian equations, that is, integer triples (x, y, z) satisfying equations of the form

where the coefficients a, b, c, d, f are integers and we assume that a, c, and ac are not square.

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[4]A. Baker and H. Davenport . On the equations 3x2 − 2 = y2 and 8x2 − 7 = z2. Quart. J. Math. Oxford Ser. (2) 20 (1969), 129137.

[8]E. Brown . Sets in which xy + k is always a square. Math. Comp. 45 (1985), 613620.

[9]C. M. Grinstead . On a method of solving a class of Diophantine equations. Math. Comp. 32 (1978), 936940.

[10]P. Kiss . On common terms of linear recurrences. Acta Math. Acad. Sci. Hungar. 40 (1982), 119123.

[13]M. Mignotte . Intersection des images de certaines suites récurrentes linéaires. Theoret. Comput. Sci. 7 (1978), 117122.

[24]D. Zagier . Large integral points on elliptic curves. Math. Comp. 48 (1987), 425436

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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