Theoretical Statistics and Mathematics Unit, ISI Delhi

August 14, 2019 (Wednesday) ,
3:30 PM at Webinar

Speaker:
Shanta Laishram,
ISI Delhi

Title:
Terms of Binary Recurrence Sequences which are products of factorials

Abstract of Talk

A conjecture of Hickerson states that the equation $n!=a_1!a_2!\cdots a_k!$ with $2\leq a_k\leq a_{k-1}\leq \cdots \leq a_2\leq a_1\leq n-2$ in positive integers implies $n\leq 16$. This is open. For a binary
recurrence sequence $\{U_n\}_{n\ge 0}$, we show that the largest $n$ for which $|U_n|=m_1!m_2!\cdots m_k!$ with $11$, then the equation $X_k=n!$ implies $k=1$. This is a joint work with F. Luca and M. Sias.