Question

Definition. Let g be in G and g 0 and g not a unit. If every divisor of g is either a unit or an associate of g, then g is prime in G; if g is not prime in G (thus g has a divisor different from g, ig, -g, or - ig), then g is composite. Exercise 1.73. The Gaussian integers can be partitioned into four noninter- secting classes: 0, the units, the primes, and the composites. Exercise 1.74. The numbers 1 +i, 1 +2i, 3, 7, 11, and 19 are all prime in G. The numbers 1 +5i, 2, 5, and 13 are all composite in G. (Hint: Suppose re neither a nor b is a unit. Then N(1 +1) -2 N(a)N(b), etc.)

Answer 1

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