On the Negative Pell Equation
y2=54x2-5

V. Pandichelvi; P. Sivakamasundari; M.A. Gopalan

doi:https://doi.org/10.14445/22315373/IJMTT-V21P502

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 21 | Number 1 | Year 2015 | Article Id. IJMTT-V21P502 | DOI : https://doi.org/10.14445/22315373/IJMTT-V21P502

On the Negative Pell Equation y2=54x2-5

V. Pandichelvi, P. Sivakamasundari, M.A. Gopalan

Abstract

The negative pell equation represented by the binary quadratic equation y2=54x2-5 is analyzed for its non-zero distinct integer solutions. A few interesting relations among the solutions are presented employing the solutions of the equation under consideration. The integer solutions for a few choices of hyperbola and parabola are obtained.

Keywords

Binary Quadratic, Hyperbola, Parabola, Integral Solutions, Pell Equation 2010 Mathematics subject classification: 11D09

References

[1] Ahmet Tekcan, The pell equation 2 2 2 t x (k k)y 2 ”, World Academy of science, Engineering and Technology, 2008,19,(697- 701).
[2] Ahmet Tekcan , Betw Gezer and Osman Bizim, On the integer solutions of the pell Equation 2 2 t x dy 2 ”,World Academy of science, Engineering and Technology 2007,1, (522-526).
[3] Dickson.L.E., History of Theory of numbers, vol.2:Diophantine Analysis, New York, Dover, 2005.
[4] Gopalan M.A.,G.sumathi,S.vidhyalakshmi, Observations on the hyperbola 2 2 t x 19y 3 ”, Scholars Journal of the Engineering and Technology,(2014), Vol:2(2A):152-155.
[5] Gopalan M.A., S.vidhyalakshmi and A.Kavitha, On the integral solution of the Binaryquadratic equation 2 2 2 x 15y 11 ”, Scholars Journal of the Engineering and Technology, 2014,Vol 2(2A),156-158.
[6] Merve Guney, Solutions of the pell equations 2 2 2 2 t x (a b 2b)y 2 , when N ( 1, 4) ”,Mathematica Aeterna , 2012, Vol 2, no.7 (629-638) .
[7] Mollin.R.A and Anitha srinivasan, A Note on the negative pell equation ”, International Journal of Algebra, 2010 ,Vol 4,no .19,919-922.
[8] Sangeetha.V, M.A.Gopalan and Manju Somanath, On the integral solutions of the pell equation 2 2 t x 13y 3 ”,International journal of appield Mathematical research, 2014,Vol .3, issue 1 (58-61).
[9] M.A.Gopalan,S.Vidhyalakshmi,N.Thiruniraiselvi, A study on the Hyperbola 8 31 2 2 y x ”,International Journal of Latest Research in Science and Technology,2013,2(1),454-456
[10] M.A.Gopalan,S.Vidhyalakshmi,T.R.UshaRani,S.Mallika, Observations on 12 3 2 2 y x ”,Bessel Journal of Mathematics,2012,2(3),153- 158.
[11] S.Vidhyalakshmi,T.R.UshaRani,S.Mallika,V,Kumari, Observations on the negative pellian 86 5 2 2 y x ”, International Journal of Applied Research,2015,1(3),86-87.

Citation :

V. Pandichelvi, P. Sivakamasundari, M.A. Gopalan, "On the Negative Pell Equation y2=54x2-5," International Journal of Mathematics Trends and Technology (IJMTT), vol. 21, no. 1, pp. 16-20, 2015. Crossref, https://doi.org/10.14445/22315373/IJMTT-V21P502