Problem 709

Erdős Problem #709: declared status 'open'. Formalized: no. Let $f(n)$ be minimal such that, for any $A=\{a_1,\ldots,a_n\}\subseteq [2,\infty)\cap\mathbb{N}$ of size $n$, in any interval $I$ of $f(n)\max(A)$ consecutive integers there exist distinct $x_1,\ldots,x_n\in I$ such that $a_i\mid x_i$. Obtain good bounds for $f(n)$, or even an asymptotic formula. Prize: no. Tags: number theory.