Fibonacci Numbers with a Prescribed Block of Digits

Pavel Trojovský
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Pavel Trojovský: Department of Mathematics, Faculty of Science, University of Hradec Králové, 500 03 Hradec Králové, Czech Republic

Mathematics, 2020, vol. 8, issue 4, 1-7

Abstract: In this paper, we prove that F 22 = 17711 is the largest Fibonacci number whose decimal expansion is of the form a b … b c … c . The proof uses lower bounds for linear forms in three logarithms of algebraic numbers and some tools from Diophantine approximation.

Keywords: Fibonacci numbers; digits; linear forms in logarithms; Baker–Davenport (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (4)

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