On the Ternary Cubic Equation 3(x2+y2) – 2xy + 4(x+y) + 4 = 51z3
Manju Somanath1, V. Sangeetha2, M. A. Gopalan3, M. Bhuvaneshwari4
1Dr. Manju Somanath, Assistant Professor, Department of Mathematics, National College, Trichy, Tamilnadu, India.
2Prof. V. Sangeetha, Asst. Prof., Department of Mathematics, National College, Trichy, Tamilnadu, India.
3Dr. M. A. Gopalan, Professor, Department of Mathematics, SIGC, Trichy, Tamilnadu, India.
4M. Bhuvaneshwari, M.Phil., Scholar, Department of Mathematics, SIGC , Trichy, Tamilnadu, India.
Manuscript received on April 30, 2015. | Revised Manuscript received on May 05, 2015. | Manuscript published on May 15, 2015. | PP: 29-31 | Volume-3 Issue-6, May 2015. | Retrieval Number: F0859053615/2015Β©BEIESP
Open Access | Ethics and Policies | Cite | Mendeley
Β© The Authors. Published By: Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)

Abstract: The non-homogeneous ternary cubic Diophantine equation given by πŸ‘ 𝒙 𝟐 + π’š 𝟐 βˆ’ πŸπ’™π’š + πŸ’ 𝒙 + π’š + πŸ’ = πŸ“πŸπ’› πŸ‘ is considered. Different patterns of non-zero distinct integer solutions to the above equation are obtained. For each of these patterns, a few interesting relations between the solutions and the special figurate numbers are obtained.
Keywords: Non-homogeneous, ternary cubic Diophantine equation, integer solutions, polygonal numbers, pyramidal numbers. 2010 Mathematics Subject Classification: 11 D 25.