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Thread: Freshman's Dream Subtraction Version? (a-b)^p = a^p - b^p ?

  1. #1

    Freshman's Dream Subtraction Version? (a-b)^p = a^p - b^p ?

    Hello All,

    I am trying to prove the insolvability of quintics, and I am now working on finite fields.

    I have proved Freshman's dream (a+b)^p = a^p + b^p for field with char = p, and that is obvious.

    However, I have seen a couple of authors use (a-b)^p = a^p - b^p in some of the proofs for finite fields. While p is odd, this is certainly right, but what if p = 2? How can this subtraction version of Freshman's dream be true in general?

    Thanks!!!

    Regards,
    Bosco

  2. #2
    Elite Member
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    17,571
    Quote Originally Posted by boscomanilow128 View Post
    Hello All,

    I am trying to prove the insolvability of quintics, and I am now working on finite fields.

    I have proved Freshman's dream (a+b)^p = a^p + b^p for field with char = p, and that is obvious.

    However, I have seen a couple of authors use (a-b)^p = a^p - b^p in some of the proofs for finite fields. While p is odd, this is certainly right, but what if p = 2? How can this subtraction version of Freshman's dream be true in general?

    Thanks!!!

    Regards,
    Bosco
    Abel-Ruffini proved that long time ago!
    “... mathematics is only the art of saying the same thing in different words” - B. Russell

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