[Math] prove that $n >2$ and $n$ is a prime then $n$ is odd

prime numbers

$n > 2$ and $n$ is a prime number then $n$ is odd.

Prove by contradiction
assume $n$ is even
then there is some $k\in\Bbb N, n = 2k$
then $n >2, 2k > 2 , k > 1$

Is this a sufficient proof?

Best Answer

To write a proof by contradiction, you must assume the premise and the negation of the conclusion:

Assume there exists an even prime $n > 2$. So $n = 2k$ where $k>1$ is an integer. (Here you can use your work showing why $k$ must be greater than 1).

Hence $n$ has at least two factors greater than or equal to $2$: $2,$ and $k \geq 2$. Hence...

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