Generalized Sierpi\'nski Numbers
A Sierpi\'nski number is a positive odd integer $k$ such that $k \cdot 2^n + 1$ is composite for all positive integers $n$. Fix an integer $A$ with $2 \le A$. We show that there exists a positive odd integer $k$ such that $k\cdot a^n + 1$ is composite for all integers $a \in [2, A]$ and all $n...
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| Format: | Artikel |
| Sprache: | eng |
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| Zusammenfassung: | A Sierpi\'nski number is a positive odd integer $k$ such that $k \cdot 2^n +
1$ is composite for all positive integers $n$. Fix an integer $A$ with $2 \le
A$. We show that there exists a positive odd integer $k$ such that $k\cdot a^n
+ 1$ is composite for all integers $a \in [2, A]$ and all $n \in \mathbb{Z}^+$. |
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| DOI: | 10.48550/arxiv.2305.09219 |