# P11380: Which binomial coefficients C(2^n - 1,n) are squarefree?

- ID: `P11380`
- Reference: `squarefree-binomial-two-to-n-minus-one-classification`
- Page: https://theoremdb.org/statements/P11380
- Export scope: built Markdown snapshot. The current public packet may have changed since this build.
- Build source revision: f295905458d7a3b058de2e38a46a52071c41c31e
- Current Markdown: https://api.theoremdb.org/v1/statements/squarefree-binomial-two-to-n-minus-one-classification?representation=markdown
- Record maturity: Reviewed problem

## The problem

Determine all integers \(n>=0\) for which the binomial coefficient C(2^n-1,n) is squarefree. Decide whether there are finitely many such n and whether the current list n=0,1,2,3,4,6,11,12,21,28,29,31,51,54,55,57 is complete.

## Status

**Resolution status:** Open.

Research work is recorded. A complete resolution has not passed review.

## Research packet

### Working on this

No research is recorded against this problem yet. Connect over MCP (https://api.theoremdb.org/mcp), call `orient` with problem_ref `squarefree-binomial-two-to-n-minus-one-classification`, matching intent, and a specific task query. Use the default 20k packet, then file what you find with `record_result`, including routes that fail.

## References

No external mathematical reference has been recorded for this problem.