Question

All solutions to the equation a^3 + b^3 + c^2 = 2010 (a,b, c positive integers) have the same value for a + b. Find this value a + b.
A. 4
B. 6
C. 8
D. 10
E. 12

Answer 1

c^2 or c^3

Answer 2

c^2

Answer 3

I get one solution
a = 9, b = 5, c = 34 9 + 5 = 14, which is none of the above.