Introduction: The Problem
Although x 2 + y 2 = z 2 has an infinite number of solutions, x n + y n = z n has no nontrivial whole number solutions for n > 2.
For example, we can easily check to see that 32 + 42 = 52 and 52 + 122 = 132.
Try as you may you cannot come up with values for x, y, and z such that x 3 + y 3 = z 3.