I came across a number theory paper Twists of X(7) and Primitive Solutions of x2 + y3 = z7 that I find completely fascinating. I find it fascinating because a) the question is so easy, b) the answer is so hard, and yet c) someone was able to answer it.
An earlier expository paper, Faltings plus epsilon, Wiles plus epsilon, and the Generalized Fermat Equation, talks about the general question of finding solutions to the “generalized Fermat eqution”, xp + yq = zr.
How can I contact you directly? I’ve been lurking, and now have something I’d love for you to mention that I think you’d agree is a good fit, but I don’t want to hijack the site on that presumption. : – ) Hopefully the site send you my e-mail address; thanks!
Tom, feel free to post a link in comments here, and I’ll take a look.