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Math Help - quadratic residues

  1. #1
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    quadratic residues

    is there a quick method to find all the quadratic residues mod p where p is prime?

    I know that there would be p-1/2 values but how do i find them?
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  2. #2
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    Re: quadratic residues

    You can just work out x^2 mod p for x=1,2,3,4,5....(p-1)/2.

    They will be distinct.

    x_i^2\equiv x_j^2 \mod p \Rightarrow (x_i-x_j)(x_i+x_j)\equiv 0 \mod p
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  3. #3
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    Re: Quadratic residues

    It may help to know that the set of all quadratic residues \mod p is a subgroup of index 2 of \mathbb Z_p^\times, the multiplicative group of the integers \mod p. I've been thinking about this recently and trying to develop a group-theoretic approach to results about quadratic residues; I'll keep you informed about further progress I make.
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