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http://hdl.handle.net/10077/8302
Title: | On repdigits as product of consecutive Fibonacci numbers | Authors: | Marques, Diego Togbé, Alain |
Keywords: | Fibonacci; repdigits; sequences (mod m) | Issue Date: | 2012 | Publisher: | EUT Edizioni Università di Trieste | Source: | Diego Marques and Alain Togbé, "On repdigits as product of consecutive Fibonacci numbers", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 44 (2012), pp. 393–397 | Series/Report no.: | Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics 44 (2012) |
Abstract: | Let (F$_{n}$)$_{n\geq0}$ be the Fibonacci sequence. In 2000, F. Luca proved that F10 = 55 is the largest repdigit (i.e. a number with only one distinct digit in its decimal expansion) in the Fibonacci sequence. In this note, we show that if Fn · · · F$_{n+(k-1)}$ is a repdigit, with at least two digits, then (k, n) = (1, 10). |
Type: | Article | URI: | http://hdl.handle.net/10077/8302 | ISSN: | 0049-4704 |
Appears in Collections: | Rendiconti dell'Istituto di Matematica dell'Università di Trieste: an International Journal of Mathematics vol.44 (2012) |
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