Abstract
The purpose of this paper is to study generalized Fibonacci and Lucas sequences. We first introduce generalized Lucas sequences. Section 2 contains a list of elementary relationships about generalized Fibonacci and Lucas sequences. In Section 3, we give a generalization of the Binet’s formulas of generalized Fibonacci, Lucas sequences and its applications. Section 4 is devote to derive many identities and congruence relations for generalized Fibonacci, Lucas sequences by using operator method.
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