A published paper or arXiv preprint answers the main question of Erdős Problem #769 (theorem erdos_769 in formal-conjectures) in full (proof, disproof, or the exact value asked for) with no hypotheses beyond the problem's own.

The problem, as stated in formal-conjectures (Apache 2.0):

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? The `c(n) \gg n^n` conjecture is **false**: for odd `n`, one can tile the unit `n`-cube into `k` homothetic cubes for every `k ≥ U(n)` with `U(n)/n^n → 0`, so `c(n)/n^n → 0` along odd dimensions and no absolute constant lower-bounds it. Determining good bounds for `c(n)` in general remains open.