Integral representations for Mersenne and Horadam-Fermat numbers
In this note we first derive integral representations for Mersenne numbers $M_{kn}$ and Horadam-Fermat numbers $\mathcal{F}_{kn}$, then we use those to provide integral representations for Mersenne numbers $M_{kn+r}$ and Horadam-Fermat numbers $\mathcal{F}_{kn+r}$, where $n\in\mathbb{Z}_{>0}=\{1,...
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| Published in | Journal of Engineering Technology and Applied Sciences Vol. 9; no. 3; pp. 185 - 200 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
31.12.2024
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| Online Access | Get full text |
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| Summary: | In this note we first derive integral representations for Mersenne numbers $M_{kn}$ and Horadam-Fermat numbers $\mathcal{F}_{kn}$, then we use those to provide integral representations for Mersenne numbers $M_{kn+r}$ and Horadam-Fermat numbers $\mathcal{F}_{kn+r}$, where $n\in\mathbb{Z}_{>0}=\{1,2,3,\ldots\}$ is a non-negative integer, $k\in\mathbb{Z}_{>0}=$ $\{1,2,3,\ldots\}$ is an arbitrary but fixed positive integer, while $r\in\mathbb{Z}_{\geqslant0}$ is an arbitrary but fixed non-negative integer. |
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| ISSN: | 2548-0391 2548-0391 |
| DOI: | 10.30931/jetas.1553048 |