{"schema":"vela.problem-packet.v0.1","problem":541,"statement":"Let $a_1,\\ldots,a_p$ be (not necessarily distinct) residues modulo $p$, such that there exists some $r$ so that if $S\\subseteq [p]$ is non-empty and\\[\\sum_{i\\in S}a_i\\equiv 0\\pmod{p}\\]then $\\lvert S\\rvert=r$. Must there be at most two distinct residues amongst the $a_i$?","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)"}