Erdős Problem 22: status mismatch (repo=solved, erdosproblems.com=formally solved)

The status of [Erdős problem 22](https://www.erdosproblems.com/22) appears to have changed.

- **[This repo](http://github.com/google-deepmind/formal-conjectures/blob/main/FormalConjectures/ErdosProblems/22.lean)**: `solved` (in `FormalConjectures/ErdosProblems/22.lean`)
- **[erdosproblems.com/22](https://www.erdosproblems.com/22)**: `formally solved`

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

Start by reading FormalConjectures/ErdosProblems/22.lean and checking the current status of problem 22 on erdosproblems.com. Verify whether the external status is accurate, then update the @[category research ...] annotation if needed; done means the repository status matches the verified source.

Written by the indexing model from the issue text.