{"schema":"vela.problem-packet.v0.1","problem":863,"statement":"Let $r\\geq 2$ and let $A\\subseteq \\{1,\\ldots,N\\}$ be a set of maximal size such that there are at most $r$ solutions to $n=a+b$ with $a\\leq b$ for any $n$. (That is, $A$ is a $B_2[r]$ set.)Similarly, let $B\\subseteq \\{1,\\ldots,N\\}$ be a set of maximal size such that there are at most $r$ solutions to $n=a-b$ for any $n\\geq 1$. If $\\lvert A\\rvert\\sim c_rN^{1/2}$ as $N\\to \\infty$ and $\\lvert B\\rvert \\sim c_r'N^{1/2}$ as $N\\to \\infty$ then is it true that $c_r\\neq c_r'$ for $r\\geq 2$? Is it true that $c_r'<c_r$?","status":"solved","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}