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Math Help - What exactly does this mean?

  1. #1
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    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.)
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  2. #2
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    Quote Originally Posted by padsinseven View Post
    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.
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