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Thread: About an identiy

  1. #1
    Member
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    About an identiy

    Hi Everybody,

    First of all thank you for your time.

    Is it know when the next identity holds?
    $\displaystyle
    A^s-B^s=(A-B)^s
    $

    $\displaystyle
    A, B, s \in Z$

    Links with more resources on this identity would be grateful

    Thank you a lot
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  2. #2
    Super Member Gamma's Avatar
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    Iowa City, IA
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    In a field with characteristic p it is true that
    $\displaystyle (a+b)^p=a^p+b^p$, you just use the binomial formula to see why all the cross terms cancel out. For instance $\displaystyle \mathbb{Z}_p$ is an example of a field of characteristic p.
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  3. #3
    Member
    Joined
    May 2009
    Posts
    77
    Yes sorry,
    This was a little bit dummy question, the actual issue was

    $\displaystyle
    |\frac{(A-B)^s}{A^s-B^s}| \leq 1
    $

    $\displaystyle
    A,B,s \in \mathbb{Z}
    $

    Which this is obvious for any A,B and for s>1

    Anyway thank you
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