Question

write the set of all integers whose cube is an even integer

Answer 1

You have 2 cases. n1=2k for some integer k, and n2 = 2j+1 for some integer j. If you take n1, and cube it, you get 8k^3 which is even, so all evens are in that set. Now n2 squared is 8j^3 + 12j^2 + 6j + 1= 2(4j^3 +6j^2 +3j) +1 which is odd, so no odd numbers have even cube. Thus the answer is all even numbers.

Answer 2

{2n : n ¢ Z}

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