> Edit: to clarify further as to what I want to know: people have been telling me that LLMs cannot solve problems that is not in their training data already. Is this really true or not?

That is not true and those people are dumb. You may be on Bluesky too much.

If your training data is a bunch of integer additions and you lossily compress this into a model which rediscovers integer addition, it can now add other numbers. Was that in the training data?