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Math Help - Quadratic Reciprocity

  1. #1
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    Quadratic Reciprocity

    Question:

    Solve the quadratic congruence x^2=11(mod 35).

    [Hint: after solving x^2=11(mod 5) and x^2=11(mod 7), use the Chinese
    remainder theorem.]
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  2. #2
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    1. What x satisies x^2= 11 (mod 5)?
    You can answer that by "brute strength": 1^2= 1, 2^2= 4, 3^2= 9= 4 (mod 5), 4^2= 16= 1 (mod 5) (Aha!).

    2. What x satisfies x^2= 11 (mod 7)?
    Do the same thing as above.

    Now, what is the "Chinese remainder theorem"?
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  3. #3
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    Quote Originally Posted by cathwelch View Post
    Question:

    Solve the quadratic congruence x^2=11(mod 35).

    [Hint: after solving x^2=11(mod 5) and x^2=11(mod 7), use the Chinese
    remainder theorem.]
    You know the factors of 35 and you obviously know the CRT, but I do not understand the basis of the question. Are you looking for a simple answer, or a method to solve it?
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  4. #4
    Senior Member TheAbstractionist's Avatar
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    Quote Originally Posted by HallsofIvy View Post
    1. What x satisies x^2= 11 (mod 5)?
    You can answer that by "brute strength": 1^2= 1, 2^2= 4, 3^2= 9= 4 (mod 5), 4^2= 16= 1 (mod 5) (Aha!).
    I wonder why you didnít go Aha! three numbers earlier.
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  5. #5
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    Just not very bright!
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