Problem 936

Erdős Problem #936: declared status 'open'. Formalized: yes. Are$$2^n\pm 1$$and$$n!\pm 1$$powerful (i.e. if $p\mid m$ then $p^2\mid m$) for only finitely many $n$? Current best: Cushing and Pascoe [CuPa16] have shown the answer to the second question is yes assuming the abc conjecture - in fact, for any fixed $k\geq 0$, there are only finitely many $n$ and powerful $x$ such that $\lvert x-n!\rvert \leq k$. Prize: no. OEIS: A146968. Tags: number theory.