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I understand why this is true, but I have no idea on how I'd go about proving it by writing a detailed structured proof.

Since a prime number is a integer, I started off like this:

Assume n in Z
    Assume n > 2 and is a prime
        Then...?

I also know that for a number to be even, it has to be divisble by 2. And if n is divisible by 2, then it can't be a prime number (exception is 2 = 2 x 1).

But how would I write this out formally?

Thank you!

dfeuer
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muros
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  • Why do you need a "formal" statement of something so obvious? If it is even, it has a factor other than itself and 1, and hence is not prime. Words work just fine...fancy notation would actually obscure your arguement here. A proof does not become false just because it is written in english instead of set theory/mathematical logic. Those formalisms are intended to allow precision in very abstract and/or nuanced contexts. It would be overkill here. –  Nov 06 '13 at 21:37
  • I agree with Eupraxis1981. With a statement so 'trivial', no proof is needed. – Christopher K Nov 06 '13 at 21:39
  • Please do not blank out questions on this site, including your own. If you wish, you can hit the "flag" link below your question to send a message to the moderators. – dfeuer Nov 07 '13 at 05:37

1 Answers1

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Assume $n>2$ is even. As $n$ is even we can write $n=2k$ with some integer $k$. From $n>2$ we obtain $k=\frac n2>1$, hence $n=2k$ is a nontrivial factorization, hecn $n$ is not prime.

Hagen von Eitzen
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