Prove by contradiction that for any integer n if n2 is odd then n is odd.
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Consider the next statement: for any integer if is odd then n is non-odd (if n is non-odd integer then n is even)
So, if is odd then n is even
Let = 2k+1, k Z
n = 2m, m N ∪ {0}
Since 2k is even integer, then 2k+1 is odd. is also even. We came to the conclusion that an odd number is equal to the even integer number, which is false. So, assumption that ' for any integer if is odd then n is non-odd ' is false, which means that for any integer if is odd then n is odd. The statement has been proved.