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Math Help - quadratic congruence

  1. #1
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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. #2
    MHF Contributor chiph588@'s Avatar
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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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    What if p=3? Isn't that different?
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  4. #4
    MHF Contributor chiph588@'s Avatar
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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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