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Properties of \(k\)-Fibonacci and \(k\)-Lucas octonions. (English) Zbl 1448.11034

Summary: We investigate some binomial and congruence properties for the \(k\)-Fibonacci and \(k\)-Lucas hyperbolic octonions. In addition, we present several well-known identities such as Catalan’s, Cassini’s and d’Ocagne’s identities for \(k\)-Fibonacci and \(k\)-Lucas hyperbolic octonions.

MSC:

11B39 Fibonacci and Lucas numbers and polynomials and generalizations
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