OBSERVATION ON THE NEGATIVE PELLIAN EQUATION

  • M.A. Gopalan Professor, Department of Mathematics, SIGC, Trichy-620002, Tamilnadu

Abstract

The binary quadratic equation represented by the negative pellian 180 11 2 2 y  x  is analyzed for its distinct integer solutions. A few interesting relations among the solutions are also given. Employing the solutions of the above hyperbola, we have obtained solutions of other choices of hyperbolas, parabolas and special ythagorean triangle. Further, employing the integer solutions of the negative pellian equation under consideration, a few interesting relations between special polygonal numbers are obtained.

References

1. R.A.Mollin and Anitha Srinivasan “A Note On The Negative Pell Equation”, International Journal of Algebra, 2010, Vol4, no. 19, 919-922.
2. E.E.Whitford, “Some Solutions of The Pellian Equations 4 2 2 x  Ay   ” JSTOR: Annals of Mathematics, Second Series, (1913-1914). Vol. no. 1 (157-160).
3. S. Ahmet Tekcan, Betw Gezer And Osman Bizim, “On The Integer Solutions of The Pell Equation t x dy 2 2 2   ” ,
World Academy of Science, Engineering and Technology 2007,1,(522-526).
4. Ahmet Tekcan “ The Pell Equationt x (k k)y 2 2 2 2    ”, World Academy of Science, Engineering and Technology 2008,19,(697-701).
5. Merve Guney, “Solutions of the pell equations t x (a b 2b)y 2 2 2 2 2    ,when N (1,4) ” , Mathematica Aterna, 2012,Vol 2, no.7(629-638).
6. V.Sangeetha, M.A.Gopalan and Manju Somanath, “On the Integral Solutions of the pell Equation t x 13y 3 2 2   ”,International Journal of Applied Mathematical Research, 2014,Vol 3 issue 1(58-61).
7. M.A.Gopalan, G.Sumathi, S.vidhyalakshmi , “Observations on the hyperbola t x 19y 3 2 2   ” , Scholars Journal of the Engineering and Technology (2014). Vol:2(2A):152-155.
8. M.A.Gopalan, S.Vidhyalakshmi and A.Kavitha, “On The Integral Solution of the Binary Quadratic Equation x 15y 11t 2 2   ” , Scholars Journal of the Engineering and Technology, 2014,Vol 2(2A),156-158.
9. K.Meena, M.A.Gopalan, R.Karthika, On the negative pell equation 10 6 2 2 y  x  , IJMRD, VOL 2(12), 2015, 390-392
10. K.Meena, M.A.Gopalan, E.Bhuvaneshwari, On the negative pell equation 60 15 2 2 y  x  , 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, PP:123-128.
12. M.A.Gopalan, R.Presenna, N.Thiruniraiselvi, “On the negative pell equation “,proceeding of national conference (UGC Sponseored) on recent developments on ennerging 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 2015; vol 1(3): 86-87.
14. M. A. Gopalan, S. Vidhyalakshmi, E.Premalatha, S.Sofia Christinal, On the negative Pell Equation 72 8 2 2 y  x  , IJETER, Vol-4, Issue-2, PP:25-28, 2016
Published
2016-01-10
How to Cite
GOPALAN, M.A.. OBSERVATION ON THE NEGATIVE PELLIAN EQUATION. Universal Journal of Mathematics, [S.l.], v. 1, n. 1, p. 14-18, jan. 2016. ISSN 2456-1312. Available at: <http://uproonline.com/index.php/UJM/article/view/12>. Date accessed: 22 sep. 2018.
Section
Articles

Keywords

Binary quadratic; hyperbola; parabola; integral solutions; pell equation; polygonal numbers.