Is the maximum size of a set $A\subseteq \{1,\ldots,N\}$ such that $ab+1$ is never squarefree (for all $a,b\in A$) achieved by taking those $n\equiv 7\pmod{25}$? Resolved for all sufficiently large $N$: any near-maximal $A$ is contained in $\{n\equiv 7\pmod{25}\}$ or $\{n\equiv 18\pmod{25}\}$, leaving only a finite check.