To the Moon and Beyond

Are there nontrivial integer solutions to the equation xn + yn = zn for any integer n ≥ 2? How about for n > 2? Wait a minute! Is this a chapter about Fermat’s Last Theorem or about Graph Coloring? From one point of view, theorems such as The Four Color Theorem and Fermat’s Last Theorem are no more important than countless other problems in chromatic graph theory or in diophantine equations, respectively, and yet both problems are pervasive in science and culture.