Someone gave a talk proposing the idea; Should they be an author?
I think inviting the student to collaborate on a paper is only fair. Whether or not the person should be a co-author depends on the person's contribution to the final product. Originating an idea may well be enough but can only be evaluated when considering the total amount of scientific input towards the manuscript. Proposing an idea can mean anything from just a lucky shot to a question based on deep understanding of the topic. Where "your" question resides is for you to consider. There are many posts covering contributorship (a development from authorship) here on acadmia.sx so I will not repeat what these responses discuss. But, it is clear that one should require any author of a manuscript to fulfil certain criteria and not just add names without thorough consideration.

So as a summary, yes, ask the person to contribute but do not give away authorship without a contributions (and the idea may well be enough).

And a final note, if you have not done so, also make sure you have not independently duplicated the other persons work if the person has continued working on the idea after graduation.