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Math Help - Irreducible factorization in number ring.

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    Irreducible factorization in number ring.

    In the quadratic number ring Z[\sqrt{2}] find an irreducible factorization of the elements 4+\sqrt{2} and 6+\sqrt{2}.
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  2. #2
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    Quote Originally Posted by featherbox View Post
    In the quadratic number ring Z[\sqrt{2}] find an irreducible factorization of the elements 4+\sqrt{2} and 6+\sqrt{2}.
    4+\sqrt{2}=(2+\sqrt{2})(3-\sqrt{2}) and 6+\sqrt{2}=(2+\sqrt{2})(5-2\sqrt{2}). note that, since the norm of the factors are prime numbers, they are irreducible.
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