Problem 365

Erdős Problem #365: declared status 'open'. Formalized: no. Do all pairs of consecutive powerful numbers $n$ and $n+1$ come from solutions to Pell equations? In other words, must either $n$ or $n+1$ be a square? Is the number of such $n\leq x$ bounded by $(\log x)^{O(1)}$? Prize: no. OEIS: A060355, A060859, A175155. Tags: number theory.