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On the Negative Pell Equation y2=45x2-11

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The binary quadratic equation represented by the negative pellian y2=45x2-11 is analyzed for its distinct integer solutions. A few interesting relations among the solutions are also given. Further, employing the solutions of the above hyperbola, we have obtained solutions of other choices of hyperbolas, parabolas and special Pythagorean triangle.


International Journal of Pure Mathematical Sciences (Volume 16)
M.A. Gopalan et al., "On the Negative Pell Equation y2=45x2-11", International Journal of Pure Mathematical Sciences, Vol. 16, pp. 30-36, 2016
Online since:
March 2016

[1] R.A. Mollin and Anitha Srinivasan A Note On The Negative Pell Equation, International Journal of Algebra, Vol4, no. 19, 2010, 919-922.

[2] E.E. Whitford, Some Solutions of The Pellian Equations , JSTOR: Annals of Mathematics, Second Series,. Vol. no. 1, (1913-1914) (157-160).

[3] S. Ahmet Tekcan, Betw Gezer And Osman Bizim, On The Integer Solutions of The Pell Equation , , World Academy of Science, Engineering and Technology 1, 2007 (522-526).

[4] Ahmet Tekcan The Pell Equation , World Academy of Science, Engineering and Technology, 19, 2008 , (697-701).

[5] Merve Guney, Solutions of the pell equations , when, Mathematica Aterna, Vol 2, no. 7, 2012, (629-638).

[6] V. Sangeetha, M.A. Gopalan and Manju Somanath, On the Integral Solutions of the pell Equation , International Journal of Applied Mathematical Research, , Vol 3 issue 1, 2014 (58-61).

[7] M.A. Gopalan, G. Sumathi, S. vidhyalakshmi , Observations on the hyperbola , , Scholars Journal of the Engineering and Technology. Vol: 2(2A), 2014, 152-155.

[8] M.A. Gopalan, S. Vidhyalakshmi and A. Kavitha, On The Integral Solution of the Binary Quadratic Equation , , Scholars Journal of the Engineering and Technology, Vol 2(2A), 2014, 156-158.

[9] K. Meena, M.A. Gopalan, R. Karthika, On the negative pell equation , IJMRD, VOL 2(12), 2015, 390-392.

[10] K. Meena, M.A. Gopalan, E. Bhuvaneshwari, On the negative pell equation , Scholars Bulletin, VOL 1(11), 2015, 310-316.

[11] M. A. Gopalan, S. Vidhyalakshmi, J. Shanthi, D. Kanaka, On the negative Pell Equation , SJPMS, Vol-2, Issue-2A, 2015, PP: 123-128.

[12] M.A. Gopalan, R. Presenna, N. Thiruniraiselvi, On the negative pell equation , Proceedings of National Conference (UGC Sponseored) on recent developments on emerging fields in pure and applied mathematics, ReDeEM, March 2015, 138-144.

[13] M.A. Gopalan, S. Vidhyalakshmi , T.R. Usha Rani , V. Kumari, " Observations on the negative pellian , International Journal of Applied Research; vol 1(3): 2015, 86-87.

[14] L.J. Mordell., Diophantine equations, Academic Press, New York, (1969).

[15] Bhatia, B.L. and Supriya Mohanty, Nasty numbers and their characterizations, Mathematical Education, 34-37, July-Sep., (1985).

[16] Bhanumurthy, T.S., A modern introduction to Ancient Indian Mathematics, New Age International Publishers limited, New Delhi, (1995).

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