This analysis determines distinct integer solutions in homogeneous ternary quadratic equations, suggesting practical solution patterns.
This paper aims at determining many non-zero distinct integer solutions to the homogeneous ternary quadratic Diophantine equation ax²+by²=(a+b)(c²+ab)z², where a,b are non-zero distinct positive integers and the product a*b is square-free. Substitution technique and factorization method are utilized to obtain the patterns of solutions in integers for the given homogeneous ternary quadratic equation.
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J.Shanthi et al. (2026) studied this question.
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