The non-homogenous cubic Diophantine equation with four unknowns represented by is analysed for its pattern of stringifies integral solutions. A few properties among the solutions and some special polygonal numbers are presented.
Introduction
Conclusion
In this analysis, the cubic diophantine equation for its non-zero distinct integral solutions in three different patterns are explored and few interesting properties are determined. To conclude, one may search for solving the cubic problem under consideration as well as cubic diophantine equation with many variables.
References
[1] Dickson L.E, “ History of the theory of numbers”, Chelsia Publishing Co, Sol II, New York 1952.
[2] Cira, Octavian, and FlorentinSmarandache. Solving Diophantine Equations. Infinite Study, 2014.
[3] Carmichael.R.D, “The theory of Numbers and Diophantine Analysis”, Dover Publications, New York,1959.
[4] JanakiDr G. “ Explorationsin Diophantine Equations”, B P International, 2023.
[5] Telangs S.G, “ Number Theory ,Tata McGraw-Hill Publishing Company, New Delhi 1996
[6] Janaki, G and P. Saranya. \"On the ternary Cubic Diophantine equation International Journal of Science and Research-online 5.3 (2016): 227-229.
[7] Janaki, G and M. Krishnaveni \"On the Integer Solutions of the Homogeneous Biquadratic Diophantine Equation.\" International Journal of Engineering Science 7275 (2016).
[8] Janaki, G and P. Saranya \"On the Ternary Cubic Diophantine Equation \" International Journal of Science and Research-Online 5.3 (2016): 227-229.
[9] Janaki G, Saranya C, ‘‘Integral solutions of the Ternary Cubic Equation ”, International Journal for Research in Applied science and Engineering and Technology vol-4, Issues 3, Page No: 665-669, March 2017.
[10] Janaki G and C. Saranya. \"Integral Solutions of the Non-Homogeneous Sixtic Equation with three unknown .\" Int. J. Sci. Res. in Multidisciplinary Studies Volume- 6.3 (2020).
[11] Janaki G, GowriShankari A , ‘‘Properties of the Ternary Cubic Equation ’’,International Journal for Research in Applied Science and Engineering Technology , volume 10, Issues III, Page No: 231-234, August 2022.
[12] Saranya C and P. Kayathri \"Integral Solutions of the Ternary Cubic Equation \", International Journal for Research in Applied Science and Engineering Technology , volume-10, Issues I, January 2022
[13] Vidhyalakshmi S, Gopalan MA, “On Finding Integer Solutions to Non-homogeneous Ternary Cubic Equation ”, Journal of Advanced Education and Sciences 2 (4) 28-31, 2022.
[14] Janaki G, and M. Aruna \"On Integer Solutions of the Ternary Quadratic Equation \", International Journal for Research in Applied Science and Engineering Technology , volume-11, Issues III, March 2023
[15] Janaki G, ShanmugaPriya S, “An Analysis on the Ternary Cubic Diophantine Equation “International Journal for Research in Applied Science and Engineering Technology, Volume-11, Issues III, March 2023.