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Math Help - Quadratic primes

  1. #1
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    Quadratic primes

    Question 1)
    Prove that there are infinitely many prime in Q[sqrt(d)] .
    Hint: It is almost identical to the proof that there are infinitely many prims in Z.

    Question 2)
    Find a prime factorization of 6 in Q[ sqrt(-1)] ?

    Hi Perfecthacker,
    Could you please teach me how to solve these questions? Thank you very much.
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  2. #2
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    Question 2)
    Find a prime factorization of 6 in Q[ sqrt(-1)] ?
    We can non-trivally factor 6 as 2*3.
    Now,
    2=(1+i)(1-i)
    But three cannot be factored because it is not of the form 4k+1.
    Thus,
    6=3(1+i)(1-i)
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