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I am having a hard time understanding this question. I have never had any number theory and so I am lost on how to start this proof. The question is as follows.

Prove that every prime $p$ greater than $2$ satisfies $p \bmod 8 = r$, where $r$ is $1, 3, 5$, or $7$.

Any help would be greatly appreciated. Thanks.

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    Welcome to math.se Karol. One way to approach this problem is with a mathematicians best friend, the contrapositive. The contrapositive of the proposition "P, therefore Q" is the equivalent proposition "Not Q, therefore not P". For example, if I asked you to show that if $n^2$ is even, then $n$ must be even, it may be hard. It's contrapositive is "If n is odd (not even), then $n^2$ is odd (not even)" which is more easily seen to be true. Here, you can try showing this instead: If $p$ is an integer greater than 2 with $p \equiv 0,2,4,6 \mod 8$, then $p$ is not prime."2012-09-26
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    Thank you for your suggestion. I am afraid I do not understand it. I have never worked with mod's before or number theory problems.I do not quite understand what this means.2012-09-26

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