Fibonacci or Lucas numbers which are products of two repdigits in base \(b\) (Q2052817)
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scientific article; zbMATH DE number 7434788
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Fibonacci or Lucas numbers which are products of two repdigits in base \(b\) |
scientific article; zbMATH DE number 7434788 |
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Fibonacci or Lucas numbers which are products of two repdigits in base \(b\) (English)
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29 November 2021
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In the paper under review the authors find all the Fibonacci numbers and Lucas numbers which are products of two rep-digits in base \(b\), where \(2\le b\le 10\) is an integer. The largest solutions are \(F_{12}=144=4_8\cdot (44)_{8}\) and \(L_{15}=1364=2_4\times (22222)_4\). The proof uses linear forms in logarithms à la Baker and reduction techniques based on continued fractions such as the Baker-Davenport reduction lemma.
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Fibonacci number
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Lucas number
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repdigit
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Diophantine equations
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linear forms in logarithms
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