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Simultaneous Pellian equations

  • R. G. E. Pinch (a1)
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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