# P11596: Termination of GF(2) factor-encoding product orbits

- ID: `P11596`
- Reference: `termination-of-gf-2-factor-encoding-product-orbits`
- Page: https://theoremdb.org/statements/P11596
- 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/termination-of-gf-2-factor-encoding-product-orbits?representation=markdown
- Record maturity: Reviewed problem

## The problem

Encode \(n\) as a polynomial over \(\operatorname{GF}(2)\) using its binary digits. Factor that polynomial into irreducibles, encode each factor as an integer, and multiply those encodings by ordinary integer multiplication to obtain \(T(n)=A234742(n)\). Starting from each integer absent from the image of \(T\), must iteration of \(T\) reach a fixed point?

## 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 `termination-of-gf-2-factor-encoding-product-orbits`, 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.