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Volume:2, Issue: 7, 2008 Page No: 501 - 504

International Journal of Engineering, Mathematical and Physical Sciences

ISSN: 2517-9934

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DOI:10.5281/zenodo.1335224 BibTeX JSON

The Proof of Two Conjectures Related to Pell-s Equation x2 −Dy2 = ± 4

Let D ≠ 1 be a positive non-square integer. In this paper are given the proofs for two conjectures related to Pell-s equation x2 -Dy2 = ± 4, proposed by A. Tekcan.
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References:
[1] A.Tekcan, The Pell Equation x2 −Dy2 = ┬▒ 4, Applied Mathematical
Sciences, vol.1, 2007, no.8, pp. 363-369.
[2] J.J.Tattersall, Elementary Number Theory in Nine Chapters, Cambridge
University Press, 2005.
[3] H.M.Edward, Fermat-s Last Theorem: A Genetic Introduction to
Algebraic Number Theory, Corrected reprint of the 1977 original.
Graduate Texts in Mathematics, 50, Springer-Verlag, 1996.
[4] P.Kaplan, K.S.Williams, Pell-s Equation x2 − my2 = −1, −4 and
Continued Fractions, Jour.Number Theory. 23(1986), pp. 169-182.
[5] A.Tekcan, Pell Equation x2 −Dy2 = 2 II", Bulletin of the Irish
Mathematical Society 54 (2004), pp. 73-89
[6] K.Mathews, "The Diophantine Equation x2 −Dy2 = 4", D > 0
Expositiones Math., 18 (2000), pp. 323-331.
[7] R.A.Mollin, A.J.Poorten, H.C.Williams, Halway to a Solution of x2
−Dy2 = −3", Journal de Theorie des Nombres Bordeaux, 6 (1994), pp.
421-457.
[8] N.Koblitz, A Course in Number Theory and Cryptography. Graduate
Texts in Mathematics, Second Edition, Springer 1994.