Pell and Pell-Lucas numbers as difference of two repdigits
Let \( \{P_{n}\}_{n\geq 0} \) be the sequence of Pell numbers defined by \( P_0=0 \), \( P_1 =1\) and \( P_{n+2}= 2P_{n+1} +P_n\) for all \( n\geq 0 \) and let \( \{Q_{n}\}_{n\geq 0} \) be its companion sequence, the Pell-Lucas numbers defined by \( Q_0=Q_1 =2\) and \( Q_{n+2}= 2Q_{n+1} +Q_n\) for a...
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| Published in | arXiv.org |
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Cornell University Library, arXiv.org
12.10.2023
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| Abstract | Let \( \{P_{n}\}_{n\geq 0} \) be the sequence of Pell numbers defined by \( P_0=0 \), \( P_1 =1\) and \( P_{n+2}= 2P_{n+1} +P_n\) for all \( n\geq 0 \) and let \( \{Q_{n}\}_{n\geq 0} \) be its companion sequence, the Pell-Lucas numbers defined by \( Q_0=Q_1 =2\) and \( Q_{n+2}= 2Q_{n+1} +Q_n\) for all \( n\geq 0 \) . In this paper, we find all Pell and Pell-Lucas numbers which can be written as difference of two repdigits. It is shown that the largest Pell and Pell-Lucas numbers which can be written as difference of two repdigits are $$P_6=70= 77-7 \quad\quad \hbox{and} \quad\quad Q_7 = 478=555-77.$$ |
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| AbstractList | Let \( \{P_{n}\}_{n\geq 0} \) be the sequence of Pell numbers defined by \( P_0=0 \), \( P_1 =1\) and \( P_{n+2}= 2P_{n+1} +P_n\) for all \( n\geq 0 \) and let \( \{Q_{n}\}_{n\geq 0} \) be its companion sequence, the Pell-Lucas numbers defined by \( Q_0=Q_1 =2\) and \( Q_{n+2}= 2Q_{n+1} +Q_n\) for all \( n\geq 0 \) . In this paper, we find all Pell and Pell-Lucas numbers which can be written as difference of two repdigits. It is shown that the largest Pell and Pell-Lucas numbers which can be written as difference of two repdigits are $$P_6=70= 77-7 \quad\quad \hbox{and} \quad\quad Q_7 = 478=555-77.$$ |
| Author | Edjeou, Bilizimbeye Faye, Bernadette |
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| Snippet | Let \( \{P_{n}\}_{n\geq 0} \) be the sequence of Pell numbers defined by \( P_0=0 \), \( P_1 =1\) and \( P_{n+2}= 2P_{n+1} +P_n\) for all \( n\geq 0 \) and let... |
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| Title | Pell and Pell-Lucas numbers as difference of two repdigits |
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