{"schema":"vela.problem-packet.v0.1","problem":540,"statement":"Is it true that if $A\\subseteq \\mathbb{Z}/N\\mathbb{Z}$ has size $\\gg N^{1/2}$ then there exists some non-empty $S\\subseteq A$ such that $\\sum_{n\\in S}n\\equiv 0\\pmod{N}$?","status":"solved","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A034463","name":"Maximal number of residue classes mod n such that no subset adds to 0.","terms":"0,1,1,2,2,3,3,3,4,4,4,4,4,5,5,5,5,5,5,6,6,6,6,6,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,9,8,9,9,9,9,9,9,9,9,10,9,10,10,10,10,1","url":"https://oeis.org/A034463"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}