Representing primes as sum of two squares

It is a famous theorem due to Fermat that every prime 1 mod 4 can be written as sum of two squares of positive integers. On the other hand, it is not possible to represent primes 3 mod 4 as sum of two squares. The latter fact is reasonable easier to prove (Fermat’s little theorem immediately proves it).

But the proof that every prime 1 mod 4 can be written as sum of two squares is quite nontrivial. The proof I learned yesterday in Elementary Number Theory course was so beautiful and mysterious that I wrote it up in LaTeX and posted here.

Enjoy!

Advertisements
This entry was posted in Uncategorized. Bookmark the permalink.

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