Abstract: The focus of this paper is to obtain patterns of integer solutions to homogeneous ternary quadratic diophantine equation given by .The process of obtaining Pythagorean triples from the integer solutions of the considered equation is exhibited.

Keywords: Homogeneous quadratic, Ternary quadratic , Integer solutions, Pythagorean triples , Substitution technique, Factorization method.

| DOI: 10.17148/IARJSET.2024.11910