Proofs by contradiction.

You are probably familiar with this example of the Pythagorean Theorem: 3^2 + 4^2 = 5^2. In contrast to this, prove that there do not exist three consecutive positive integers a, b, c such that a^3 + b^3 = c^3

Problem 9: You are probably familiar with this example of the Pythagorean Theorem: 32 + 42 = 52. In contrast to this, prove that there do not exist three consecutive positive integers a, b, c such that a3 + b3 : c3