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The Zeckendorf decomposition of certain Fibonacci-Lucas products. (English) Zbl 0942.11012

The Zeckendorf decomposition of any positive integer as a sum of positive-subscripted, distinct, nonconsecutive Fibonacci numbers is always possible and unique. In this paper the Zeckendorf decomposition is established for products \(mab\), where \(m\) is a positive integer \(\leq 5\), and \(a\) and \(b\) are certain Fibonacci and/or Lucas numbers. Also products \(a^2b\) are considered.

MSC:

11B39 Fibonacci and Lucas numbers and polynomials and generalizations
11A63 Radix representation; digital problems
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