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Math Help - Quadratic Residues

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    Quadratic Residues

    Determine the set of primes for which 11 is a quadratic residue.
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    Senior Member TheAbstractionist's Avatar
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    First, note that 11 is a quadratic residue mod 2 (e.g. 1^2\equiv11\,(\bmod\,2)).

    Let p and q be odd primes. There is a result (equivalent to the law of quadratic reciprocity) that says that (11\,|\,p)=(11\,|\,q) if and only if p\equiv\pm q\,(\bmod\,44). So you only have to determine all odd primes p < 44 for which (11\,|\,p)=1 All other odd primes for which 11 is a quadratic residue will congruent to plus or miinus one of these.
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    Thanks

    Thanks.

    Do you know where I can find more information on the result that you quoted? I've never seen this before.
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    Senior Member TheAbstractionist's Avatar
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    Quote Originally Posted by Cairo View Post
    Do you know where I can find more information on the result that you quoted? I've never seen this before.
    I came across it in H.E. Rose, A Course in Number Theory, p.67:

    Theorem 2.2 Let p and q be distinct odd primes and a\ge1. The quadratic reciprocity law is equivalent to

    if p\equiv\pm q\,(\bmod\,4a) then (a/p)=(a/q).
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