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Circulants and the factorization of the Fibonacci-like numbers. (English) Zbl 1132.11009

Using circulant matrices, their determinants and eigenvalues the authors give factorizations of the Fibonacci-like numbers \(U_n\) and their squares \(U^2_n\). \(U_n\) is defined by \(U_n= pU_{n-1}+ qU_{n-2}\), \(n\geq 2\), \(U_0= 0\), \(U_1= 1\) and arbitrary integers \(p\), \(q\).

MSC:

11B39 Fibonacci and Lucas numbers and polynomials and generalizations
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References:

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