Claims

../

2016_11_03_cushing_pascoe: Cushing and Pascoe show that, assuming the abc conjecture, only finitely many powerful numbers lie within a fixed distance of a factorial, which answers the factorial half of Problem 936 conditionally.

2020_05_15_crowdmath: CrowdMath shows that, assuming the abc conjecture, k^n + r is powerful only finitely often for fixed coprime positive k and r, which covers 2^n + 1 and, through (n!)^r + k, also n! + 1; the paper does not treat 2^n - 1.

---