ON THE HOMOGENEOUS CONE 2 2 2 3x − 8 y = 25z
DOI:
https://doi.org/10.48165/Keywords:
Ternary quadratic, homogeneous quadratic, homogeneous cone, integerAbstract
This paper aims at determining non-zero distinct integer solutions satisfying the homogeneous cone represented by the ternary quadratic equation 2 2 2 3x − 8y = 25z . A few interesting relations among the solutions are presented. A general formula for generating sequence of integer solutions to the given cone based on a given solution is illustrated.
References
Dickson, L.E. (1952). History of Theory of Numbers, Vol. II, Chelsea Publishing Company, New York.
Mordell, L.J. (1970). Diophantine Equations, Academic Press, New York.
Carmicheal, V. (1959). The Theory of Numbers and Diophantine Analysis, Dover Publications, New York.
Sumathi, G. and Deebika, B. (2017). Integral Points On The Cone 2 2 2
x − 3y =16z , Journal of
Mathematics and Informatics, Vol. 11, 47-54.
Mallika, S. and Hema, D. (2017). On The Ternary Quadratic Diophantine Equation 2 2 2
y = 3x + 2z ”,
Journal of Mathematics and Informatics, Vol. 10, 157-165.
Vidhyalakshmi, S. and Yogeshwari, S. (2017). On The Non-Homogeneous Ternary Quadratic Diophantine Equation 2 2 2
x − 2y = 9z , Journal of Mathematics and Informatics, Vol. 10, 125-133.
Kavitha, A. and Sasipriya, P. (2017). A Ternary Quadratic Diophantine Equation 2 2 2
x + y = 56 z ,
Journal of Mathematics and Informatics, Vol. 11, 103-109.
Gopalan, M.A. and Vidhyalakshmi, S., and Kavitha, A. (2012). Integral points on the homogeneous cone 2 2 2
z = 2x − 7y ”, Diophantus J. Math.,1 (2), 127-136.
Gopalan, M.A., Vidhyalakshmi, S., Uma Rani, J. (2013). Integral points on the homogeneous cone 2 2 2
x + 4y = 37z , Cayley J. Math., 2(2), 101-107.
Gopalan, M.A., Sivagami, B. (2013). Integral points on the homogeneous cone 2 2 2
z = 39x + 6y ,
IOSR Journal of Mathematics, 8(4), 24-29.
Gopalan, M.A., Vidhyalakshmi, S. and Maheswari, D. (2014). Integral points on the homogeneous cone 2 2 2
x + 3y = 35z , Indian Journal of Science , Vol. 7, 6-10.
Meena, K., Vidhyalakshmi, S., Gopalan, M.A. and Aarthy Thangam, S. (2014). Integer solutions on the homogeneous cone 2 2 2
x + 3 y = 28z , Bull. Math. &Stat. Res., Vol. 2, Issue 1, 47-53.
Gopalan, M.A., Vidhyalakshmi, S. and Thiruniraiselvi, N. (2015). Observations on the ternary quadratic Diophantine equation 2 2 2
x + 9y = 50z , International Journal of Applied Research, 1(2),
-53.
Downloads
Published
Issue
Section
How to Cite
