Logo
All Random Solved Random Open
OPEN
Let $f(n)$ denote the minimal $m$ such that \[n! = a_1\cdots a_t\] with $a_1<\cdots <a_t=a_1+m$. What is the behaviour of $f(n)$?
Erdős and Graham write that they do not even know whether $f(n)=1$ infinitely often (i.e. whether a factorial is the product of two consecutive integers infinitely often).