# P11474: Does every A349876 residue-map orbit reach a multiple of 3?

- ID: `P11474`
- Reference: `totality-of-the-a349876-residue-map`
- Page: https://theoremdb.org/statements/P11474
- 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/totality-of-the-a349876-residue-map?representation=markdown
- Record maturity: Reviewed problem

## The problem

For n not divisible by 3, write \(n=3k\)+r with r in {1,2} and replace n by 5k+r+3. Does every nonnegative starting value eventually reach a multiple of 3?

## 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 `totality-of-the-a349876-residue-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.