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Problem 936 — Erdős Problems

Problem 936

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 $n$ ?

Source: erdosproblems.com/936

Number theory
Powerful numbers

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Open

No claim settles this problem.

Open, the site's label (OPEN). No claim settles the question; both claim pages are conditional on the abc conjecture.

Cr20: P. A. CrowdMath, Applications of the abc conjecture to powerful numbers. arXiv:2005.07321 (2020).
CuPa16: D. Cushing and J. E. Pascoe, Powerful numbers and the ABC-conjecture. arXiv:1611.01192 (2016).

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Status: Open
Topics: Number theory
Powerful numbers
In the wiki: Wiki page