Section14.4Exercises

  1. Look up the concepts of "Gaussian moat", "Gaussian zoo", and/or "Gaussian prime spiral" and tell me what you think!
  2. Look for a pattern, similar to the one we found for sums of squares, for which primes can be written in the form \(x^2+3y^2\). Prove that the primes not of this form are impossible.
  3. Look up “Eisenstein integers”. Can you find any interesting theorems along these lines which they prove? What would Eisenstein primes look like?