OBSERVATION ON THE BIQUADRATIC EQUATION WITH FIVE UNKNOWNS
2(x - y)(x3 + y3) + x4 - y4 = 2(z2 - w2)p2
By
J. Shanthi, S. Vidhyalakshmi and M. A. Gopalan
Department of Mathematics, Shrimati Indira Gandhi College,
Aliated to Bharathidasan University, Trichy, Tamil Nadu, India- 620002
Email: shanthivishvaa@gmail.com, vidhyasigc@gmail.com, mayilgopalan@gmail.com
(Received: July 15, 2023; In format: August 28, 2023; Revised: September 03, 2023;
Accepted: September 13, 2023)
DOI: https://doi.org/10.58250/jnanabha.2023.53207
Abstract
This paper focuses on obtaining non-zero integer quintuples (x,y, z,w, p) satisfying the bi-quadratic equation with ve unknowns given by 2(x - y)(x3 + y3) + x4 - y4 = 2(z2 - w2)p2. Various patterns of solutions are obtained by reducing the given bi-quadratic equation to solvable ternary quadratic equation through employing linear transformations.
2020 Mathematical Sciences Classification: 11D25.
Keywords and Phrases: homogeneous bi-quadratic, quinary bi-quadratic, integer solutions.