# Thread: What exactly does this mean?

1. ## What exactly does this mean?

I don't know exactly what this means
The problem states

Z(sqrt-5)= ((a+b(sqrt-5) such that a,b are elements of Z) contained in C

What exactly does Z(sqrt-5) mean? I have never seen this before and I have to do a proof that looks similar.This is the proof I have to do if that sheds any light. Any tips on the notation or the proof would be appreciated.

Let S = {a + b sqrt(-5): a, b in Z}. Prove that
the number 6 in S has two fundamentally different factorizations
into primes of S. (Thus , unlike Z, the set S does not enjoy the property
of unique prime factorization.)

2. Originally Posted by padsinseven
I don't know exactly what this means
The problem states

Z(sqrt-5)= ((a+b(sqrt-5) such that a,b are elements of Z) contained in C

What exactly does Z(sqrt-5) mean? I have never seen this before and I have to do a proof that looks similar.This is the proof I have to do if that sheds any light. Any tips on the notation or the proof would be appreciated.

Let S = {a + b sqrt(-5): a, b in Z}. Prove that
the number 6 in S has two fundamentally different factorizations
into primes of S. (Thus , unlike Z, the set S does not enjoy the property
of unique prime factorization.)
$\mathbb{Z}[\sqrt{-5}]$ all means is the integral domain $\{ a+bi\sqrt{5} |a,b\in \mathbb{Z} \}$. Your goal is to prove that this domain is not a unique factorization domain.