A Glimpse on Integral Solutions of Ternary Uniform Second Degree Equation 𝟓 (𝐱𝟐 + 𝐲𝟐) − 𝟑𝑥𝑦 = 𝟐𝟎𝟎𝟎𝑧𝟐

Objectives: Many integer solutions to ternary homogeneous quadratic given by are determined. Various choices of integer solutions are secure from beginning to end employing linear modifications and used to simplify expressions. Methods: Different transformations are utilized to determine many solutions in integers for the considered polynomial equation. Findings: Five distinct transformations are applied to obtain choices of integral solutions for the considered second-degree equation having three unknowns. Novelty: The equation in the title has been reduced to a solvable ternary quadratic equation by employing suitable transformation. Mathematics Subject Classification: 11D09 Keywords: Quadratic having three unknowns, Homogeneous quadratic, Integer Solutions, Ternary Quadratic Equation, Pair of equations