Complementary Families of the Fibonacci-Lucas Relations
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math.NT
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familiesfibonacci-lucasidentitybasicbestbijectivecomplementaryfibonacci
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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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