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Math Help - 3 irreducible in Z[sq.rt.-5]

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    3 irreducible in Z[sq.rt.-5]

    How can you show that 3 is irreducible in Z[(-5^(1/2)]?
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    Quote Originally Posted by tomnook View Post
    How can you show that 3 is irreducible in Z[(-5^(1/2)]?
    You write 3 = (a+bi\sqrt{5})(c+di\sqrt{5}).
    Expand the RHS and compare coefficients.
    Now argue that a=\pm 1, b=0 or c=\pm 1, d=0.
    That would 3 cannot be factored properly and non-trivially.
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    of course! thanks!
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