FOM Proof Challenge

Hello FOMMIES!

By the start of class on Friday, September 25th, you should post on your blogs an attempt at proving the following:

\forall a \in \mathbb{Z}, a \text{ is even } \iff a^2 \text{ is even}

I should also point out that the definition of even is this: an integer z \in \mathbb{Z} is even if there exists n \in \mathbb{Z} such that z = 2n.

Note that this is not an assignment — you are not required to post this.  However, if everyone posts an attempt at this proof by the start of class on Friday, then your mid-term will be a very lovely experience.

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