Main post link -> http://blog.brilliant.org/2013/02/26/gaussian-integers-ii/
Learn about the classification Gaussian Primes over at the Blog.
Decompose \(6-12i\) into a product of primes.
Prove that no integer of the form \(n^2+1\) can have a prime divisor of the form \(4k+3 \). Hint: Use Theorem 3.
How many Gaussian integers of norm 2005 are there? Hint: Theorem 4.
(*) Show that a positive integer can be written as a sum of two complete squares if and only if each of its prime factors of the form \(4k+3\) appears in even power.
Feel free to take a crack at these questions and share your thoughts.