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Math Help - Number Theory: Units

  1. #1
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    Number Theory: Units

    Two obvious units in Z[sqrt(d)] are 1 and -1. For d = 3, 5, 6, 7, 8, 10, 11, and 12, find a unit in Z[sqrt(d)] other than 1 and -1 and list for each unit what its inverse is. What can be said about units in Z[sqrt(d)] if d < 0 and d is not equal to -1.?

    I found units for d = 3, 5, and 6:

    2 + sqrt(3)
    9 + 4 * sqrt(5)
    5 + 2 * sqrt(6)

    But I can't find a way to find to find them other than just trying out different numbers.

    Edit: I've figured it out and no longer need help.
    Last edited by TheHowlingLung; October 31st 2012 at 02:55 AM.
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