Answer to Question #86948 in Abstract Algebra for RAKESH DEY

Question

Let d€N, where d not equal to 1 and d is not divisible by the square of a prime. Prove that N:Z[√d] such that N union {0} : N(a+b√d)=|a^2-db^2| satisfies the following properties for x,y € Z[√d]:
1) N(x)=0 that implies x=0
2) N(x)=1 implies that x is a unit
3) N(x) is prime implies that x is irreducible in Z[√d]

Answer 1

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