Analysis constructs 3-pairs of generalized fibonacci and lucas numbers, suggesting novel solutions for diophantine equations.
This work uses a general integer parameter p to try to generalise $3$-pairs of subsequences of Fibonacci numbers and Lucas numbers. In this study, we focus on constructing $3$-pairs of generalized Lucas and Fibonacci-type combinatorial p-entities that satisfy a more general quadratic Diaphantine equation of the kind x²-Ny²= ± k2. Separate sections present a variety of Discrete Mathematical features of the combinatorial p-entities.
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Rangarajan et al. (2025) studied this question.
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