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Math Help - number theory algebra help

  1. #1
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    number theory algebra help

    For any a, b ,  \in R let a * b denote ab + a + b.
    Show that if a* b = -1 then either a = -1 or b = -11.

    Am not sure where to start, from here.
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  2. #2
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    Re: number theory algebra help

    I assume that R means \mathbb{R}, the set of real numbers.

    (If R stands for a generic ring, you'll need to specify that it's a domain.)

    I also assume that your "b = -11" is a typo - that you intended "b = -1"

    a*b = -1 implies ab + a + b = -1.

    Now write that as "a, b stuff" = 0, and it will actually factor, and from there lead you to your result.
    Last edited by johnsomeone; October 17th 2012 at 02:01 PM.
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  3. #3
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    Re: number theory algebra help

    Hint: ab + a + b + 1 = (a+1)(b+1).
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  4. #4
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    Re: number theory algebra help

    Yes thank you, it was a typo b=-1 not 11
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