Erdős Problem 109: status mismatch (repo=solved, erdosproblems.com=formally solved)

The status of [Erdős problem 109](https://www.erdosproblems.com/109) appears to have changed.

- **[This repo](http://github.com/google-deepmind/formal-conjectures/blob/main/FormalConjectures/ErdosProblems/109.lean)**: `solved` (in `FormalConjectures/ErdosProblems/109.lean`)
- **[erdosproblems.com/109](https://www.erdosproblems.com/109)**: `formally solved`

Please verify and update the `@[category research ...]` annotation if appropriate.

Start with FormalConjectures/ErdosProblems/109.lean and inspect its @[category research ...] annotation. Compare the repository status with the linked erdosproblems.com/109 page, then update the annotation if the external status is confirmed. Done means the issue's status mismatch is resolved in the Lean file.

Written by the indexing model from the issue text.