This work was produced within the Bolzano project (https://bolzano.app), using AI systems for mathematical research and manuscript preparation. The listed authors contributed to the project and the preparation of this release. The manuscript received only limited human checking.

Text origin: primarily AI-generated.
Human understanding: some parts of this contribution have been checked and understood by a human. The manuscript received only limited human checking.
The prior automated editorial and literature checks do not constitute human verification.

The manuscript answers the eventual-existence binomial-divisibility question of Erdős–Straus, distinct from Egyptian fractions. Earlier density-one results are cited; absolute priority is not certified.
