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

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## Details

### 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(*x*^{2} – *y*^{2}) + 3(*x* + *y*) =10*z*^{4}. 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

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## Cite this paper

APAVidhyalakshmi, S., Gopalan, M. A.,Thangam, S. A. & Özer, Ö. (2019). On ternary biquadratic Diophantine equation 11(*x*^{2} – *y*^{2}) + 3(*x* + *y* ) =10*z*^{4} . Notes on Number Theory and Discrete Mathematics, 25(3), 65-71, doi: 10.7546/nntdm.2019.25.3.65-71.

Vidhyalakshmi, S., Gopalan, M. A.,Thangam, S. A. & Özer, Ö. “On ternary biquadratic Diophantine equation 11(*x*^{2} – *y*^{2}) + 3(*x* + *y* ) =10*z*^{4} .” Notes on Number Theory and Discrete Mathematics 25, no. 3 (2019): 65-71, doi: 10.7546/nntdm.2019.25.3.65-71.

Vidhyalakshmi, S., Gopalan, M. A.,Thangam, S. A. & Özer, Ö. . “On ternary biquadratic Diophantine equation 11(*x*^{2} – *y*^{2}) + 3(*x* + *y* ) =10*z*^{4} .” Notes on Number Theory and Discrete Mathematics 25.3 (2019): 65-71. Print, doi: 10.7546/nntdm.2019.25.3.65-71.