I thought of this problem while I was lying in bed. Zaku will no doubt complain about its relevance, but I thought it is a more interesting high school level math problem than the usual fare.

Find x and y such that x^{2 + y}2 = 1,000,000. Note that for x = 8 and y = 6, x^{2 + y}2 = 100. Do you see how to use that to find a simple solution? You can think of the (x, y) values as points in the plane.