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Math Help - Congruency equations.

  1. #1
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    Congruency equations.


    Sorry is x^2 - y^2 = 2n (for second questions)
    Last edited by mr fantastic; April 25th 2010 at 09:33 PM. Reason: Re-titled post.
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  2. #2
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    I think the second problem is wrong. for example when x = y = 3 and n = 9
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  3. #3
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    1. Then x=qk+r for some integer k. Then x^n = (qk+r)^n. Expand it. 19^n+39^n=3^n+(-1)^n. Since phi(8)=4, you only need to check n up to 4.
    2. Quadratic residues modulo 4 are only 0 and 1. So x^2-y^2 can only be 1,0,-1 modulo 4. While 2n=2 (mod 4) if n is odd. #
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