SOLUTION: Prove that the sum of the cubes if two numbers is odd if and only if one of the numbers is even and one is odd.

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Question 847109: Prove that the sum of the cubes if two numbers is odd if and only if one of the numbers is even and one is odd.
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
If both numbers are even or both numbers are odd, then the sum of their cubes will be even, since the cube of an even # is even and the cube of an odd # is odd.

If one is even and one is odd, then the sum of the cubes is odd.

Since we have exhausted all possible cases, the proof is complete.