On the surface, it seems easy. can you think of the integers for x, y, and z so that x³+y³+z³=8? sure. one answer is x = 1, y = -1, and z = 2. but what about the integers for x, y, and z so that x³+y³+z³=42?

that turned out to be much harder—as in, no one was able to solve for those integers for 65 years until a supercomputer finally came up with the solution to 42. (for the record: x = -80538738812075974, y = 80435758145817515, and z = 12602123297335631. obviously.)