---

Claim. T. H. Chan, Factors of almost squares and lattice points on circles, Int. J. Number Theory 11 (2015), no. 5, 1701--1708 (card), Theorem 2 (arXiv numbering): every sufficiently large $n=(N-a)(N+b)$ with integers $0\le a\le b\le e^{(\log n)^{2/7}}$ has at most eighteen divisors in $[\sqrt n-n^{1/4}(\log n)^{1/14},\sqrt n+n^{1/4}(\log n)^{1/14}]$. For each $C>0$, $Cn^{1/4}<n^{1/4}(\log n)^{1/14}$ once $n$ is large, so the answer to Problem 887 is yes for these $n$, with $K=18$. The site prints the factorization as $(N-a)(N-b)$; the paper's is $(N-a)(N+b)$.

Covers. The question with $n$ restricted to these numbers, a class that contains $N^2-1$, $N^2-4$ and the perfect squares.

Depends on. No page of this wiki.

Acceptance. Refereed: International Journal of Number Theory. The site labels the problem OPEN, so its commentary is not acceptance.