{"schema":"vela.problem-packet.v0.1","problem":769,"statement":"Let $c(n)$ be minimal such that if $k\\geq c(n)$ then the $n$-dimensional unit cube can be decomposed into $k$ homothetic $n$-dimensional cubes. Give good bounds for $c(n)$ - in particular, is it true that $c(n) \\gg n^n$?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A014544","name":"Numbers k such that a cube can be divided into k subcubes.","terms":"1,8,15,20,22,27,29,34,36,38,39,41,43,45,46,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73","url":"https://oeis.org/A014544"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}