Palindromic concatenations of two distinct repdigits in Narayana's cows sequence
| Autor: | Ddamulira, Mahadi, Emong, Paul, Mirumbe, Geoffrey Ismail |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Let $(N_{n})_{n\ge 0}$ be Narayana's cows sequence given by a recurrence relation $ N_{n+3}=N_{n+2}+N_n $ for all $ n\ge 0 $, with initial conditions $ N_0=0 $, and $ N_1= N_2=1 $. In this paper, we find all members in Narayana's cow sequence that are palindromic concatenations of two distinct repdigits. Our proofs use techniques on Diophantine approximation which include the theory of linear forms in logarithms of algebraic numbers and Baker's reduction method. We show that $595$ is the only member in Narayana's cow sequence that is a palindromic concatenation of two distinct repdigits in base $10$. Comment: Accepted to appear in the Bulletin of the Iranian Mathematical Society (BIMS) |
| Databáze: | arXiv |
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