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Claim. Assume the abc conjecture. Then for each fixed integer $k\ge0$ there are only finitely many powerful numbers $x$ with $|x-n!|\le k$ for some $n$ (Theorem 4.1 of D. Cushing and J. E. Pascoe, Powerful numbers and the ABC-conjecture, arXiv:1611.01192, posted 2016-11-03). Taking $k=1$, the numbers $n!+1$ and $n!-1$ are powerful for only finitely many $n$, which is the second question of Problem 936. The source card is cushing_2016_powerful_numbers_abc_conjecture.

Proof as written. Lemma 4.2 proves the case $k=0$, that $n!$ is powerful only finitely often, from Bertrand's postulate, and Lemma 4.3 proves the half of Theorem 4.1 for numbers $n!+k$. The other half, for numbers $n!-k$, is left to the reader as Exercise 4.4, so the conditional answer for $n!-1$ rests on that exercise.

Hypothesis. The abc conjecture: for every $\epsilon>0$ there is a constant $K_\epsilon$ such that coprime positive integers $a+b=c$ satisfy $c<K_\epsilon\operatorname{rad}(abc)^{1+\epsilon}$. It is unproved, so the claim gives no unconditional answer and settles no standing of the problem.

Depends on. No other wiki page; the claim rests on the cited preprint and the hypothesis stated above.

Acceptance. None. The paper is an arXiv preprint with no journal version found, and the site labels the problem OPEN, so the site's commentary crediting the paper is not acceptance.