Erdős Problem #769

Erdős problem #769 · erdosproblems.com/769

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.

Result

Disproved(see note)

Status

Partial result

AI contribution

AI-discovered

Method

Construction

Field

Discrete Geometry

Posed by

—

Year posed

—

Years open

—

Solved

2026-07-13

Model

GPT-5.6 starships (Claude Fable 5 reviewer)

Vendor

OpenAI / Anthropic

Collaborators

—

Verification

Lean-verified

Publication

Announced

Significance

10 / 100*

Disclosed cost

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Wikipedia

No dedicated article