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# [Brilliant Blog] Gaussian Integers II

Learn about the classification Gaussian Primes over at the Blog.

Test Yourself

1. Decompose $$6-12i$$ into a product of primes.

2. Prove that no integer of the form $$n^2+1$$ can have a prime divisor of the form $$4k+3$$. Hint: Use Theorem 3.

3. How many Gaussian integers of norm 2005 are there? Hint: Theorem 4.

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.

Note by Peter Taylor
4 years, 5 months ago