Problem 930

Erdős Problem #930: declared status 'open'. Formalized: yes. Is it true that, for every $r$, there is a $k$ such that if $I_1,\ldots,I_r$ are disjoint intervals of consecutive integers, all of length at least $k$, then$$\prod_{1\leq i\leq r}\prod_{m\in I_i}m$$is not a perfect power? Prize: no. Tags: number theory.