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Thread: square modulo the prime...

  1. April 12th 2010, 04:10 AM #1
    NikoBellic
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    square modulo the prime...

    Determine whether 219 is a square modulo the prime 383.
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  2. April 12th 2010, 07:10 AM #2
    tonio
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    Quote Originally Posted by NikoBellic View Post
    Determine whether 219 is a square modulo the prime 383.

    Using Jacobi's symbol and quadratic reciprocity:

    \binom {219}{383}=\binom{3}{383}\binom{73}{383}=-\binom{383}{3}\binom{383}{73} =-\binom{2}{3}\binom{18}{73}=-(-1)\binom{2}{73}\binom{9}{73}=1\cdot 1\cdot 1=1
    Tonio
    Last edited by tonio; April 12th 2010 at 07:37 AM.
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