Problem Statement
Let $\epsilon>0$. Is it true that, for all large $n$, the number of divisors of $n$ in $(n^{1/2},n^{1/2}+n^{1/2-\epsilon})$ is $O_\epsilon(1)$?
Categories:
Number Theory Divisors
Progress
Erdős attributes this conjecture to Ruzsa. Erdős and Rosenfeld [ErRo97] proved that there are infinitely many $n$ such that there are four divisors of $n$ in $(n^{1/2},n^{1/2}+n^{1/4})$.See also [887].
Source: erdosproblems.com/886 | Last verified: January 19, 2026