{"schema":"vela.problem-packet.v0.1","problem":530,"statement":"Let $\\ell(N)$ be maximal such that in any finite set $A\\subset \\mathbb{R}$ of size $N$ there exists a Sidon subset $S$ of size $\\ell(N)$ (i.e. the only solutions to $a+b=c+d$ in $S$ are the trivial ones). Determine the order of $\\ell(N)$.In particular, is it true that $\\ell(N)\\sim N^{1/2}$?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A143824","name":"Size of the largest subset {x(1),x(2),...,x(k)} of {1,2,...,n} with the property that all differences |x(i)-x(j)| are distinct.","terms":"0,1,2,2,3,3,3,4,4,4,4,4,5,5,5,5,5,5,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,10,10,10","url":"https://oeis.org/A143824"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}