[Brilliant Blog] Gaussian Integers II

Main post link -> http://blog.brilliant.org/2013/02/26/gaussian-integers-ii/

Learn about the classification Gaussian Primes over at the Blog.

Test Yourself

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.

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Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$