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Fibonacci numbers as mixed concatenations of Fibonacci and Lucas numbers
Mathematica SlovacaAbstractLet (Fn)n≥0and (Ln)n≥0be the Fibonacci and Lucas sequences, respectively. In this paper we determine all Fibonacci numbers which are mixed concatenations of a Fibonacci and a Lucas numbers. By mixed concatenations ofaandb, we mean the both concatenationsabandbatogether, whereaandbare any two nonnegative integers.
Altassan, Alaa, ALAN, Murat
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Fibonacci numbers with Fibonacci numbers as subscripts
2018The original solution of Problem B-1203 in the problem section of this journal. It was acquired to prove two equalities for the sums with the Fibonacci numbers or the Lucas numbers whose indices are again the Fibonacci numbers and the Lucas numbers, respectively.
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A Logarithmic Formula for Fibonacci Numbers
The Fibonacci Quarterly, 1966zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Applications of Fibonacci Numbers
Mathematics of Computation, 1989H. C. W. +3 more
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Abstract The Fibonacci numbers are introduced and carefully developed together with a bit of biography of Fibonacci himself. He is best known for promoting the use of Hindu-Arabic numerals in Europe and especially for his “rabbit problem” which introduces the Fibonacci numbers. Of special interest is the decimal expansion for 1/89 having
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On the Generalization of the Fibonacci Numbers
The Fibonacci Quarterly, 1975openaire +2 more sources
Fibonacci-Riesel and Fibonacci-Sierpiński numbers
The Fibonacci Quarterly, 2008Florian Luca, V. Janitzio Mejía Huguet
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Fibonacci numbers which are concatenation of three Fibonacci or Lucas numbers
Punjab University Journal of MathematicsIn this note, we show that there is no Fibonacci number that can be expressed as a concatenation of three Fibonacci or Lucas numbers under a certain constraint. That is, we solve to the Diophantine equations Fn = 10d+lFm1 + 10lFm2 + Fm3 and Fn = 10d+lLm1 + 10lLm2 + Lm3 in non-negative integers (n, m1, m2, m3) with m2 ≤ m1, where d and l represent the ...
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