Keywords:-
Keywords:
Homogeneous cone ,Ternary quadratic ,Integer solutions
Article Content:-
Abstract
This paper aims at determining non-zero distinct integer solutions to the homogeneous cone given by . A few interesting properties between the solutions are presented.
References:-
References
1. M.A.Gopalan., and A.Vijayashankar, Integral points on the homogeneous cone ,IJIRSET,Vol 2(1), 682-685,Jan 2013.
2. M.A.Gopalan., S.Vidhyalakshmi, and V.Geetha, Lattice points on the homogeneous cone , IJESRT,Vol 2(2), 775-779,Feb 2013.
3. M.A.Gopalan., S.Vidhyalakshmi and E.Premalatha , On the Ternary quadratic Diophantine equation ,Diophantus.J.Math1(1),51-57,2012.
4. M.A.Gopalan., S.Vidhyalakshmi and A.Kavitha , Integral points on the homogeneous cone ,Diophantus.J.Math1(2),127-136,2012.
5. M.A.Gopalan and G.Sangeetha, Observations on , Antarctica J.Math., 9(4),359-362,(2012).
6. M.A.Gopalan., Manju Somanath and V.Sangeetha , Observations on the Ternary Quadratic Diophantine Equation ,Bessel J.Math., 2(2),101-105,(2012).
7. GopalanM.A., S.Vidhyalakshmi and E.Premalatha , On the Ternary quadratic equation ,Diophantus.J.Math1(2),69-76,2012.
8. GopalanM.A., S.Vidhyalakshmi and E.Premalatha, On the homogeneous quadratic equation with three unknowns , Bulletin of Mathematics and Statistics Research,Vol 1(1),38-41,2013.
9. Meena.K, GopalanM.A., S.Vidhyalakshmi and N.Thiruniraiselvi, Observations on the quadratic equation , International Journal of Applied Research , Vol 1(2),51-53,2015.
10. R.Anbuselvi and S.A. Shanmugavadivu, On homogeneous Ternary quadratic Diophantine equation , IJERA, 7(11), 22-25, Nov 2017.
11. S. Vidhyalakshmi, T. Mahalakshmi, “A Study On The Homogeneous Cone ”, International Research Journal of Engineering and Technology (IRJET), Volume 6, Issue 3, Pages 5000-5007, March 2019.
12. J.Shanthi,T.Mahalakshmi ,S.Vidhyalakshmi ,M.A.Gopalan ,”A search on Integer solutions to t6he Homogeneous Quadratic Equation with Three Unknowns IJRPR ,Vol 4 ,No 5 ,3610-3619 ,May 2023.
13. J. Shanthi and M. Parkavi, “On finding Integer solutions to the Homogeneous ternary Quadratic Diophantine equation ”,International Journal of Research Publication and Reviews, Volume 4, No. 1, pp 700-708, January 2023.
14. T. Mahalakshmi, E. Shalini ,” On Finding Integer Solutions to the Homogeneous Ternary Quadratic Diophantine Equation ”, International Journal of Research Publication and Reviews, Vol 4, no 5, pp 452-462 May 2023.
2. M.A.Gopalan., S.Vidhyalakshmi, and V.Geetha, Lattice points on the homogeneous cone , IJESRT,Vol 2(2), 775-779,Feb 2013.
3. M.A.Gopalan., S.Vidhyalakshmi and E.Premalatha , On the Ternary quadratic Diophantine equation ,Diophantus.J.Math1(1),51-57,2012.
4. M.A.Gopalan., S.Vidhyalakshmi and A.Kavitha , Integral points on the homogeneous cone ,Diophantus.J.Math1(2),127-136,2012.
5. M.A.Gopalan and G.Sangeetha, Observations on , Antarctica J.Math., 9(4),359-362,(2012).
6. M.A.Gopalan., Manju Somanath and V.Sangeetha , Observations on the Ternary Quadratic Diophantine Equation ,Bessel J.Math., 2(2),101-105,(2012).
7. GopalanM.A., S.Vidhyalakshmi and E.Premalatha , On the Ternary quadratic equation ,Diophantus.J.Math1(2),69-76,2012.
8. GopalanM.A., S.Vidhyalakshmi and E.Premalatha, On the homogeneous quadratic equation with three unknowns , Bulletin of Mathematics and Statistics Research,Vol 1(1),38-41,2013.
9. Meena.K, GopalanM.A., S.Vidhyalakshmi and N.Thiruniraiselvi, Observations on the quadratic equation , International Journal of Applied Research , Vol 1(2),51-53,2015.
10. R.Anbuselvi and S.A. Shanmugavadivu, On homogeneous Ternary quadratic Diophantine equation , IJERA, 7(11), 22-25, Nov 2017.
11. S. Vidhyalakshmi, T. Mahalakshmi, “A Study On The Homogeneous Cone ”, International Research Journal of Engineering and Technology (IRJET), Volume 6, Issue 3, Pages 5000-5007, March 2019.
12. J.Shanthi,T.Mahalakshmi ,S.Vidhyalakshmi ,M.A.Gopalan ,”A search on Integer solutions to t6he Homogeneous Quadratic Equation with Three Unknowns IJRPR ,Vol 4 ,No 5 ,3610-3619 ,May 2023.
13. J. Shanthi and M. Parkavi, “On finding Integer solutions to the Homogeneous ternary Quadratic Diophantine equation ”,International Journal of Research Publication and Reviews, Volume 4, No. 1, pp 700-708, January 2023.
14. T. Mahalakshmi, E. Shalini ,” On Finding Integer Solutions to the Homogeneous Ternary Quadratic Diophantine Equation ”, International Journal of Research Publication and Reviews, Vol 4, no 5, pp 452-462 May 2023.
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Shanthi, J., Anbuvalli, V., Gopalan, M., & Vidhyalakshmi, S. (2023). On Finding Integer Solutions to the Homogeneous Cone x^2+(k^2+2k)y^2=(k+1)^4 z^2. International Journal Of Mathematics And Computer Research, 11(7), 3555-3557. https://doi.org/10.47191/ijmcr/v11i7.09