2000 character limit reached
On members of Lucas sequences which are products of factorials (1901.01063v1)
Published 4 Jan 2019 in math.NT
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.