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On members of Lucas sequences which are products of factorials
Published 4 Jan 2019 in math.NT | (1901.01063v1)
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 $n<3\times 105$. We also give better bounds in case the roots of the Lucas sequence are real.
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