(a) If n is odd, then n cube is also odd.
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Step-by-step explanation:
If n is odd, then n3 is odd. n3 = (2k + 1)3 = 8k3 + 12k2 + 6k + 1 = 2(4k3 + 6k2 + 3k)+1. By the closure of the integers under addition and multiplication, we know that 4k3 + 6k2 + 3k is an integer. Call this integer m, so that we have n3 = 2m + 1.
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Answer:
yes if n is odd than n cube is also odd
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