I am trying to create a proof that for all integers $m$, if $m > 3$, then $m^2-4$ is not prime. I am having issue however actually figuring out how to finish it off. Here's what I have so far…
Proof: Let integer m be given. $m^2 – 4 = (m-2)(m+2)$. Suppose that $m > 3$. Since $m > 3$, $m+2 > m-2 > 1$…
Most of the examples that I have create an integer $k$ and use it to finish the proof but I'm not sure how to define it in this example. Any help would be wonderful! Thanks.
Best Answer
Hint:
$$ m^2 - 4 = (m - 2)(m + 2) $$