1. The problem statement, all variables and given/known data a^3 + b^3 + c^2 = 2012 ; a, b, and c are positive integers. 2. Relevant equations I was thinking prime factorization, but that was a bust. 3. The attempt at a solution 2012 has a beast of a prime in it (503) so I have no idea how to solve this theoretically. Help. In retrospect, factorization isn't a key element here anyway.