On The Negative Pell Equation x^2=8y^2-4
Keywords:
Binary quadratic, Pell equation, Hyperbola, Parabola, Integral solutions
Abstract
The binary quadratic equation represented by x^2=8y^2-4 the negative pellian is analyzed for its distinct integer solutions. A few interesting relations among the solutions are given. Further, employing the solutions of the above hyperbola, we have obtained solutions of other choices of hyperbolas, parabolas and special Pythagorean triangle.
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References
[1] R.A. Mollin, Anitha srinivasan, A note on the Algebra,(2010) ,4(19),919-922.
[2] E.E. Whitford,“Some Solutions of the Pellian Equations ,” JSTOR:Annals of Mathematics, Second Series 1913-1914; vol5, No.1/4, 157-160.
[3] S. Ahmet Tekcan, Betw Gezer and Osman Biim, “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 of the Pell equations when Mathematica Aterna, 2(7); (2012); 629-638..
[6] M.A. Gopalan, S. Vidhyalakshmi., T.R. Usha Rani, and S. Mallika, “Observations on ” Bessel Journal of Math, 2(3); (2012); 153-158.
[7] M.A. Gopalan, S. Vidhyalakshmi, N. Thiruniraiselvi, “A study on the Hyperbola on ”, International Journal of Latest Research in Science and Technology, 2(1), Feb(2013); 454-456.
[8] V. Sangeetha, M.A. Gopalan, Manju Somanath, “On the Integral Solutions of the pell equation ”, International Journal of Applied Mathematical Research, (2014); 3(1), 58-61.
[9] M.A. Gopalan, S. Vidhyalakshmi, G. Sumathi, “Observations on the Hyperbola on ”, Scholars Journal of the Engineering and Technology, 2(2A), (2014); 152-155.
[10] M.A. Gopalan, S. Vidhyalakshmi, A. Kavitha, “On the Integral Solution of the Binary , Quadratic Equation”, Scholars Journal of the Engineering and Technology, 2(2A), (2014); 156-158.
[11] S. Vidhyalakshmi, V. Krithika, K. Agalya, “On the negative Pell Equation ”, Proceedings of the National Conference on MATAM, Dindukal, (2015), 4-9.
[12] K. Meena, M.A. Gopalan, R. Karthika, “On the Negative Pell Equation ”, International Journal of Multidisciplinary Research and Development, 2(12); Dec (2015); 390-392.
[13] K. Meena, M.A. Gopalan, A. Rukmani, “On the Negative Pell Equation ”, Universe of Emerging Technologies and Science, Vol II, Dec (2015); Issue XII; 1-4.
[14] K. Meena, M.A. Gopalan, E. Bhuvaneswari, “On the Negative Pell Equation ”, Scholars Bulletin, 1(11); Dec (2015); 310-316.
[15] M.A. Gopalan, S. Vidhyalakshmi, R. Presenna, M. Vanitha, “Observation on the Negative Pell Equation ”, Universe Journal of Mathematics , Vol 2, Dec (2015); Issue 1; 14-. 45.
[16] M.A. Gopalan, S. Vidhyalakshmi, V. Pandichelvi, P. Sivakamasundari, Priyadharshini, “On the Negative Pell Equation ”, International Journal of pure Mathematical Science,Vol-16; (2016); 30-36.
[17] S. Vidhyalakshmi, M.A. Gopalan, E. Premalatha, S. Sofia christinal, “On the Negative Pell Equation “, International Journal of Emerging Technologies in Engineering Research(IJETER), 4(2); Feb (2016), 25-28.
[18] K. Meena, S. Vidhyalakshmi, G. Dhanalakshmi, “On the Negative Pell Equation “, Asian Journal of Applied Science and Technology (AJAST), 1(7); Aug (2017), 98-103.
[2] E.E. Whitford,“Some Solutions of the Pellian Equations ,” JSTOR:Annals of Mathematics, Second Series 1913-1914; vol5, No.1/4, 157-160.
[3] S. Ahmet Tekcan, Betw Gezer and Osman Biim, “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 of the Pell equations when Mathematica Aterna, 2(7); (2012); 629-638..
[6] M.A. Gopalan, S. Vidhyalakshmi., T.R. Usha Rani, and S. Mallika, “Observations on ” Bessel Journal of Math, 2(3); (2012); 153-158.
[7] M.A. Gopalan, S. Vidhyalakshmi, N. Thiruniraiselvi, “A study on the Hyperbola on ”, International Journal of Latest Research in Science and Technology, 2(1), Feb(2013); 454-456.
[8] V. Sangeetha, M.A. Gopalan, Manju Somanath, “On the Integral Solutions of the pell equation ”, International Journal of Applied Mathematical Research, (2014); 3(1), 58-61.
[9] M.A. Gopalan, S. Vidhyalakshmi, G. Sumathi, “Observations on the Hyperbola on ”, Scholars Journal of the Engineering and Technology, 2(2A), (2014); 152-155.
[10] M.A. Gopalan, S. Vidhyalakshmi, A. Kavitha, “On the Integral Solution of the Binary , Quadratic Equation”, Scholars Journal of the Engineering and Technology, 2(2A), (2014); 156-158.
[11] S. Vidhyalakshmi, V. Krithika, K. Agalya, “On the negative Pell Equation ”, Proceedings of the National Conference on MATAM, Dindukal, (2015), 4-9.
[12] K. Meena, M.A. Gopalan, R. Karthika, “On the Negative Pell Equation ”, International Journal of Multidisciplinary Research and Development, 2(12); Dec (2015); 390-392.
[13] K. Meena, M.A. Gopalan, A. Rukmani, “On the Negative Pell Equation ”, Universe of Emerging Technologies and Science, Vol II, Dec (2015); Issue XII; 1-4.
[14] K. Meena, M.A. Gopalan, E. Bhuvaneswari, “On the Negative Pell Equation ”, Scholars Bulletin, 1(11); Dec (2015); 310-316.
[15] M.A. Gopalan, S. Vidhyalakshmi, R. Presenna, M. Vanitha, “Observation on the Negative Pell Equation ”, Universe Journal of Mathematics , Vol 2, Dec (2015); Issue 1; 14-. 45.
[16] M.A. Gopalan, S. Vidhyalakshmi, V. Pandichelvi, P. Sivakamasundari, Priyadharshini, “On the Negative Pell Equation ”, International Journal of pure Mathematical Science,Vol-16; (2016); 30-36.
[17] S. Vidhyalakshmi, M.A. Gopalan, E. Premalatha, S. Sofia christinal, “On the Negative Pell Equation “, International Journal of Emerging Technologies in Engineering Research(IJETER), 4(2); Feb (2016), 25-28.
[18] K. Meena, S. Vidhyalakshmi, G. Dhanalakshmi, “On the Negative Pell Equation “, Asian Journal of Applied Science and Technology (AJAST), 1(7); Aug (2017), 98-103.
Published
2018-12-31
How to Cite
Gopalan, M. (2018). On The Negative Pell Equation x^2=8y^2-4. GPH - International Journal of Mathematics, 1(12), 01-09. Retrieved from https://gphjournal.org/index.php/m/article/view/139
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