On ternary biquadratic Diophantine equation
11(x2 – y2) + 3(x + y ) =10z4

S. Vidhyalakshmi, M. A. Gopalan, S. A. Thangam and Ö. Özer
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 25, 2019, Number 3, Pages 65-71
DOI: 10.7546/nntdm.2019.25.3.65-71
Full paper (PDF, 91 Kb)

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Authors and affiliations

S. Vidhyalakshmi
Department of Mathematics, Shrimati Indira Gandhi College
Trichy-620002, Tamil Nadu, India

M. A. Gopalan
Department of Mathematics, Shrimati Indira Gandhi College
Trichy-620002, Tamil Nadu, India

S. A. Thangam
Department of Mathematics, Shrimati Indira Gandhi College
Trichy-620002, Tamil Nadu, India

Ö. Özer
Department of Mathematics, Faculty of Science and Arts, Kırklareli University
Kırklareli, 39100, Turkey

Abstract

We obtain infinitely many non-zero integer triples (x, y, z) satisfying the non-homogeneous bi-quadratic equation with three unknowns 11(x2 – y2) + 3(x + y) =10z4. Various interesting properties among the values of x, y, z are presented. Some relations between the solutions and special numbers are exhibited.

Keywords

  • Ternary bi-quadratic
  • Integer solutions
  • Pell equations

2010 Mathematics Subject Classification

  • 11D25
  • 11D09

References

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Cite this paper

Vidhyalakshmi, S., Gopalan, M. A.,Thangam, S. A. & Özer, Ö. (2019). On ternary biquadratic Diophantine equation 11(x2 – y2) + 3(x + y ) =10z4 . Notes on Number Theory and Discrete Mathematics, 25(3), 65-71, DOI: 10.7546/nntdm.2019.25.3.65-71.

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