Question

2. Give a direct proof of the theorem“ If n is odd , then n^2 is odd”. ​

Answer 1

For all integers n) If n is odd, then n2 is odd. Proof: If n is odd, then n = 2k + 1 for some integer k. Thus, n2 = (2k + 1)2 = 4k2 + 4k + 1 = 2(2k2 + 2k) + 1.

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