{"schema":"vela.problem-packet.v0.1","problem":786,"statement":"Let $\\epsilon>0$. Is there some set $A\\subset \\mathbb{N}$ of density $>1-\\epsilon$ such that $a_1\\cdots a_r=b_1\\cdots b_s$ with $a_i,b_j\\in A$ can only hold when $r=s$?Similarly, can one always find a set $A\\subset\\{1,\\ldots,N\\}$ with this property of size $\\geq (1-o(1))N$?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A143301","name":"Decimal expansion of the Hall-Montgomery constant.","terms":"1,7,1,5,0,0,4,9,3,1,4,1,5,3,6,0,6,5,8,6,0,4,3,9,9,7,1,5,5,5,2,1,2,1,0,9,6,2,2,2,6,2,9,0,4,2,2,9,5,5,0,8,4,1,7,1,4,2,1,1,","url":"https://oeis.org/A143301"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}