At my college, authorship is done in order of contribution (if evident) or alphabetically. Generally, to prevent conflicts, its done alphabetically, but that's not the case here.
In that case, then you would only be considered an author if your actually wrote any of the paper. It's difficult to tell if you actually wrote part of the paper, or if you just solved the problem and they wrote the paper, but either way they did more work on the paper. You could be listed as a contributor, but not as an author. This article explains the difference.
New researchers who aspire to official authorship status may see the title of “contributor” as a relegation or demotion in rank, but for other, more experienced researchers, it may simply be a pragmatic recognition of the fact that you may have provided valuable resources but didn’t actually contribute to the writing or editing of the research paper.
Basically, you made a contribution, but you did not author all or part of the paper. That would put you as the last in-order at most, or a footnote at the least. So, we go like this:
[Name, Student], [Er, Research], [U, Yo], [Tor, Edi]