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Math Help - Quadritic residues and more

  1. #1
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    Quadritic residues and more

    (a) Determine Q240.
    (b) Determine T(U240).
    (c) Find all solutions of x^2(is congruent to) -23 (mod 240).

    I was able to figure out part (a), but I don't know what to do for part (b) and (c). I believe my solution for (a) was {1,49,119,199}

    For (a) and (b), the 240 is subscript of course.
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  2. #2
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    Quote Originally Posted by shadow_2145 View Post
    (a) Determine Q240.
    (b) Determine T(U240).
    Define what that means.

    (c) Find all solutions of x^2(is congruent to) -23 (mod 240).
    You need to solve,
    x^2 \equiv 9(\bmod 2^4)
    x^2\equiv 1(\bmod 3)
    x^2 \equiv 2(\bmod 5).

    But the third equation has no solutions.
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