Is it better for a mathematical paper to have a citation or a nice theorem + another coauthor? I'm publishing my first paper soon with three collaborators.  We made a conjecture towards the end of the paper and intended to publish with the question still open.  Another mathematician heard of the problem and found a solution to the conjecture.  Now we have two options: 


publish our current paper on our own, with the conjecture open, after which our friend would publish their solution as a separate paper, or
include their work at the end of our paper and make them a co-author.


Though our paper is pretty good already, the new work is strong and would make a nice addition, so the first option seems nice.  On the other hand, I'm an undergraduate senior (entering graduate school this Fall) and so are two of the other collaborators.  Thus it seems like adding another professor as a co-author may make my contributions (which I have worked very hard on) appear less substantial.  Also in favor of option 2: if the other professor publishes separately, the citation may make our paper look good.

What do you think?
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.