# P11963: Integer return under the 4/3 ceiling map

- ID: `P11963`
- Reference: `integer-return-under-the-4-3-ceiling-map`
- Page: https://theoremdb.org/statements/P11963
- 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/integer-return-under-the-4-3-ceiling-map?representation=markdown
- Record maturity: Reviewed problem

## The problem

Let \(f(x)=\tfrac{4}{3}\lceil x\rceil\). For every nonnegative integer \(n\), does there exist an integer \(k\ge 1\) such that the iterate \(f^k(n)\) is an integer?

## 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 `integer-return-under-the-4-3-ceiling-map`, 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.