ON THE QUINARY SURD EQUATION u3√(x² + y²) + v3√(x² + y²) = (k²+s²)R²
By
N. Thiruniraiselvi1 , R. Sathyapriya1 and M. A. Gopalan2
1Department of Mathematics, School of Engineering and Technology, Dhanalakshmi Srinivasan University,
Samayapuram, Trichy, Tamil Nadu, India- 621 112
2Department of Mathematics, Shrimati Indira Gandhi College, Affiliated to Bharathidasan University, Trichy, Tamil Nadu, India- 620 002
Email: Corresponding: thiruniraiselvin.set@dsuniversity.ac.in, drntsmaths@gmail.com, charukanishkgmail.com, mayilgopalan@gmail.com
(Received: July 23, 2023; In format: January 18, 2024; Revised: April 28, 2025; Accepted: May 15, 2025)
DOI: https://doi.org/10.58250/jnanabha.2024.55113
Abstract
This paper aims at finding different sets of solutions in integers to the surd equation u3√(x² + y²) + v3√(x² + y²) = (k²+s²)R² . Some curious observations involving figurate numbers are exhibited.
2020 Mathematical Sciences Classification: 11D99
Keywords and Phrases: Surd equation; Transcendental equation; Integral solutions; Figurate numbers.