Products of three Fibonacci numbers that are repdigits (Q6549909)
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scientific article; zbMATH DE number 7859686
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Products of three Fibonacci numbers that are repdigits |
scientific article; zbMATH DE number 7859686 |
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Products of three Fibonacci numbers that are repdigits (English)
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4 June 2024
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The authors prove that the largest instance of a product of three Fibonacci numbers being a repdigit is \(55\) (this is a product of three Fibonacci numbers, with two of such factors being \(1\)). The proof uses an approach via Baker's method to get an astronomical bound on the length (number of digits) of the repdigit in question (in this case \(3\cdot 10^{44}\)) and then Baker-Davenport reduction to reduce this bound to a small enough range in which one can find all solutions by enumeration.
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Fibonacci numbers
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Diophantine equations
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repdigits
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linear forms in logarithms
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