On members of Lucas sequences which are products of factorials

Shanta Laishram; Florian Luca; Mark Sias

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arXiv · 1901.01063

On members of Lucas sequences which are products of factorials

Shanta Laishram·Florian Luca·Mark Sias

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Abstract

Here, we show that if $\{U_n\}_{n\ge 0}$ is a Lucas sequence, then the largest $n$ such that $|U_n|=m_1!m_2!\cdots m_k!$ with $1<m_1\le m_2\le \cdots\le m_k$ satisfies $n<3\times 10^5$. We also give better bounds in case the roots of the Lucas sequence are real.

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BibTeX RIS

Shanta Laishram, Florian Luca, Mark Sias. 2019-01-04. On members of Lucas sequences which are products of factorials. https://arxiv.org/abs/1901.01063

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