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”, x^p + y^q = z^r.