Problem 928

Erdős Problem #928: declared status 'open'. Formalized: no. Let $\alpha,\beta\in (0,1)$ and let $P(n)$ denote the largest prime divisor of $n$. Does the density of integers $n$ such that $P(n)<n^{\alpha}$ and $P(n+1)<(n+1)^\beta$ exist? Prize: no. OEIS: A006530. Tags: number theory.