International Journal of Mathematics Trends and Technology
Volume 65 | Issue 7 | Year 2019 | Article Id. IJMTT-V65I7P526 | DOI : https://doi.org/10.14445/22315373/IJMTT-V65I7P526
Homogeneous ternary quadratic equation 6x2 + 7y2 = 559z2 is analysed for its integral points on it. Employing the integral solutions of the above equation, a few interesting relations between the solutions and the special numbers are also exhibited.
[1] Dickson L.E. “History of theory of numbers”, Vol-2, Diophantine analysis, New York, Dover, 2005.
[2] Mordell L.J. “Diophantine equations”, Academic press, New York, 1969.
[3] Carmichael R.D. “The theory of numbers and Diophantine analysis”, New York, Dover, 1959.
[4] Gopalan M.A, Geetha D, Lattice points on the hyperbola of two sheets x2 - 6xy + y2 +6x-2y+5=z2+4 , Impact J sci Tech : 4:23-32,2010.
[5] Gopalan M.A, Vidhyalakshmi S, Kavitha A, Integral points on the homogeneous cone z2 = 2x2 - 7y2 , The Diophantine J Math ;1(2):127 ,136,2012. .
[6] Gopalan M.A, Vidhyalakshmi S, Sumathi G, Lattice points on the hyperboloid of one sheet 4z2 = 2x2+3y2-4 ,Diophantine J Math;1(2):109 -115,2012..
[7] Gopalan M.A, Vidhyalakshmi S, Lakshmi K, Integral points on the hyperboloid of two sheets 3y2 = 7x2 - z2 +21 , Diophantine J Math ;1(2): 99 -107,2012.
[8] Gopalan M.A, Vidhyalakshmi S, Mallika S, Observations on hyperboloid of one sheet x2 + 2y2-z2 = 2 , Bessel J Math ;2(3): 221- 226,2012. .
[9] Gopalan M.A, Vidhyalakshmi S, Usha Rani T.R, Mallika S, Integral points on the homogeneous cone 6z2+3y2 - 2x2= 0 , Impact J sci Tech ;6(1): 7 -13,2012. .
[10] Gopalan M.A, Vidhyalakshmi S, Sumathi G, Lattice points on the elliptic paraboloid z= 9x2 +4y2 , Advances in Theoretical and Applied Mathematics;m7(4): 379 -385,2012..
[11] Gopalan M.A, Vidhyalakshmi S, Usha Rani T.R, Integral points on the non-homogeneous cone 2z2+4xy+8x-4z=0 , Global Journal of Mathematics and Mathematics Sciences 2012; 2(1): 61- 67 .
[12] Gopalan M.A, Vidhyalakshmi S, Lakshmi K, Lattice points on the elliptic paraboloid 16y2 +9z2 = 4x , Bessel J of Math ; s
[13] Gopalan M.A, Geetha T, HemalathaK,”On the ternary quadratic Diophantine equation 5(x2 + y2) - 2xy = 20z2 ”, International journal of multidisciplinary research and development, Vol-2, Issue: 4,211-214, April-2015.
[14] Hema.D,Mallika.S,”On the ternary quadratic Diophantine equation 5y2=3x2+2z2 ,Journal of Mathematics and informatics,Vol.10,157-165,2017.
[15] Selva Keerthana.K , Mallika.S, “On the Ternary Quadratic Diophantine equation 3(x2+y2)-5xy+2(x+y)+4=15z2 ”Journal of Mathematics and informatics,Vol. 11,21-28,2017.
Dr. S.Mallika, "On The Homogeneous Ternary Quadraticdiophantine Equation 6x2 +7y2 =559z2," International Journal of Mathematics Trends and Technology (IJMTT), vol. 65, no. 7, pp. 206-217, 2019. Crossref, https://doi.org/10.14445/22315373/IJMTT-V65I7P526
PDF 
Abstract 
Keywords 
References 
Citation