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Thread: quadratic congruence

  1. March 23rd 2010, 12:36 PM #1
    tarheelborn
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    quadratic congruence

    If p is an odd prime, what are the two solutions to x^2 == 4 (mod p) in the set {1, 2, 3, ..., p-1}?
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  2. March 23rd 2010, 02:40 PM #2
    chiph588@
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    Quote Originally Posted by tarheelborn View Post
    If p is an odd prime, what are the two solutions to x^2 == 4 (mod p) in the set {1, 2, 3, ..., p-1}?
    If p is odd, then 2^2 \equiv 4 \mod{p} and (-2)^2\equiv(p-2)^2\equiv4\mod{p} .

    So our solutions are x=2,p-2 .
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  3. March 24th 2010, 05:28 AM #3
    tarheelborn
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    What if p=3? Isn't that different?
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  4. March 24th 2010, 05:54 AM #4
    chiph588@
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    Quote Originally Posted by tarheelborn View Post
    What if p=3? Isn't that different?
    Nope, 2,3-2=1 are solutions.
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