Monday Math 32

Today we have a bit of number theory. Let n be an integer greater than one. Then if is prime, it can be expressed in the form , for some integer k.

Proof: we have that if is prime, for some integer k. The latter equation is the same as , which has a solution for integer k if and only if n is even. Now, we see that if n is odd, then is odd, and so is even. Since n>1, , and thus we see if n is odd, cannot be prime. Thus, if is prime, n is even, and so is divisible by four, and thus can be expressed in the form .

Advertisements

Tags: , ,

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s


%d bloggers like this: