Let $c(n)$ be minimal such that if $k\ge c(n)$ 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 $c(n)\gg n^n$?

gpt-erdos · GPT-5.2 Pro + Deep Research · unverified

Let $D(n)$ be the set of integers $k$ for which the unit $n$-cube can be tiled (decomposed) into $k$ smaller **homothetic** $n$-cubes, and let $c(n)$ be the least integer such that all (k\ge c(n)) lie in $D(n)$.

llm-hunter · gpt pro 5.2 · unverified

1 LLM attack(s) recorded (gpt pro 5.2); unverified.