Complementary Families of the Fibonacci-Lucas Relations
Ivica Martinjak, Helmut Prodinger

TL;DR
This paper introduces two new families of Fibonacci-Lucas identities, including a bijective proof and generating function analysis, expanding understanding of these mathematical relations.
Contribution
It presents novel Fibonacci-Lucas identities with bijective proofs and generating function approaches, enhancing the theoretical framework of Fibonacci and Lucas sequences.
Findings
Established two new families of identities
Provided bijective proofs for the identities
Analyzed the identities using generating functions
Abstract
In this paper we present two families of Fibonacci-Lucas identities, with the Sury's identity being the best known representative of one of the families. While these results can be proved by means of the basic identity relating Fibonacci and Lucas sequences we also provide a bijective proof. Both families are then treated by generating functions.
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Taxonomy
TopicsAdvanced Mathematical Theories and Applications · Advanced Combinatorial Mathematics · Mathematics and Applications
