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Math Help - congruence in integer #2

  1. #1
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    congruence in integer #2

    Prove or disprove: if a^2=b^2=mod(n) and n is prime then a=b(mod n) or a=-b(mod n).
    Last edited by mr fantastic; April 15th 2010 at 03:34 PM. Reason: Edited post title
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  2. #2
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    Quote Originally Posted by Deepu View Post
    Prove or disprove: if a^2=b^2=mod(n) and n is prime then a=b(mod n) or a=-b(mod n).

    True: a^2=b^2\!\!\!\pmod n \Longleftrightarrow (a-b)(a+b)=0\!\!\!\pmod n \Longleftrightarrow a-b=0\!\!\!\pmod n\,\,\,or\,\,\,a+b=0\!\!\!\pmod n , since n is prime.

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