We will prove the following statement:

If $$n$$ is an odd integer, then $$n squared$$ is an odd integer.

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Question $3$

$1$

First we will suppose that

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Question $3$

$2$

Then by definition of odd, we have

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Question $3$

$3$

Then it follows that

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Question $3$

$4$

We can then factor to get

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Question $3$

$5$

and since it is true that

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Question $3$

$6$

we have that $$n squared$$ is odd