Is it better for a mathematical paper to have a citation or a nice theorem + another coauthor?
I think it is not important which option makes your paper look good, but the best question here is "what is the right thing to do?"
If you are such a talented and hardworking undergraduate student who can write a publishable paper, you will certainly have a very bright future in grad school and later as a researcher. So, don't worry how your first paper is going to be evaluated or cited. Hopefully you will write better papers and you can prove yourself in the future. Regarding publishing research papers, the right thing to do is that you publish your paper as perfect as it is possible for you at the moment, which means it is better you add the solution (and one more co-author) to your paper.