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Erdős problem 769

For the least cutoff c(n)c(n) after which every kk occurs as the number of homothetic cubes in a decomposition of the unit nn-cube, is c(n)≫nnc(n) \gg n^n? The Lean proof shows c(n)=o(nn)c(n) = o(n^n) along odd dimensions.

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For the least cutoff $c(n)$ after which every $k$ occurs as the number of homothetic cubes in a decomposition of the unit $n$-cube, is $c(n) \gg n^n$? The Lean proof shows $c(n) = o(n^n)$ along odd dimensions.

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