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[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

  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

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