On Finding Integer Solutions to Non-homogeneous Ternary Cubic Equation [x^2+xy+y^2=(m^2+3n^2 ) z^3]

Authors

  • S. Vidhyalakshmi Assistant Professor, Department of Mathematics, Shrimati Indira Gandhi College, Affiliated to Bharathidasan University, Trichy, Tamil Nadu, India
  • M. A. Gopalan Professor, Department of Mathematics, Shrimati Indira Gandhi College, Affiliated to Bharathidasan University, Trichy, Tamil Nadu, India

Keywords:

cubic with three unknowns, non-homogeneous cubic, integer solutions

Abstract

The purpose of this paper is to obtain different sets of non-zero distinct integral solutions of ternary non-homogeneous cubic Diophantine equation x2+xy+y2=(m2+3n2) z3. A few properties of interest are presented.

References

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Vijayasankar A, Sharadha Kumar, Gopalan MA. On Non-Homogeneous Ternary Cubic Equation x^3+y^3+x+y=2z(2z^2-α^2+1), International Journal of Research Publication and Reviews, 2021; 2(8):592-598.

Vidhyalakshmi S, Shanthi J, Hema K, Gopalan MA. Observation on the paper entitled Integral Solution of the homogeneous ternary cubic equation x^3+y^3=52(x+y)z^2, EPRA IJMR, 2022; 8(2):266-273.

Vidhyalakshmi S, Gopalan MA, General form of integral solutions to the ternary non-homogeneous cubic equation y^2+Dx^2=αz^3, IJRPR, 2022; 3(9):1776-1781.

Vidhyalakshmi S, Gopalan MA, On Finding Integer Solutions to Non-homogeneous Ternary Cubic Equation x^2+by^2=(m^2+bn^2)z^3, IRJEdT, 2022; 4(10):22-29.

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Published

2022-10-21

How to Cite

Vidhyalakshmi, S., & Gopalan, M. A. (2022). On Finding Integer Solutions to Non-homogeneous Ternary Cubic Equation [x^2+xy+y^2=(m^2+3n^2 ) z^3]. Journal of Advanced Education and Sciences, 2(4), 28–31. Retrieved from https://dzarc.com/education/article/view/166

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