1. The problem statement, all variables and given/known data a) Let k be any integer. Prove that if k3 is even, then k is even. 2. Relevant equations 3. The attempt at a solution Proof by contradiction: If the hypothesis is true, then k3 cannot be even if k is odd. Assume k is odd: k = 2n + 1, such that n is any integer. k3 = (2n + 1)3 k3 = (2n +1)(2n +1)(2n +1) k3 = 2(k3 + 5k2 + 3k) + 1 Now, (k3 + 5k2 + 3k) is any integer. Therefore k3 is odd if k is odd, hence if k3 is even if k is even.