number-theory / Number Theory
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.
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Resolved for all sufficiently large N via a stability theorem; small N remain a finite computation (erdosproblems.com marks the problem DECIDABLE)
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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.
Resolved for all sufficiently large N via a stability theorem; small N remain a finite computation (erdosproblems.com marks the problem DECIDABLE)
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