- #1

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http://en.wikipedia.org/wiki/Quadratic_residue:"Modulo 2, every integer is a quadratic residue.

Modulo an odd prime number

*p*there are (

*p*+ 1)/2 residues (including 0) and (

*p*− 1)/2 nonresidues."

If this is to vague I apologize.

- Thread starter moriheru
- Start date

- #1

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http://en.wikipedia.org/wiki/Quadratic_residue:"Modulo 2, every integer is a quadratic residue.

Modulo an odd prime number

If this is to vague I apologize.

- #2

FeDeX_LaTeX

Gold Member

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The second line is saying that the congruence [itex]x^2 \equiv a \text{ }\left( \text{mod } p \right)[/itex] for p ≠ 2 has [itex]\frac{p+1}{2}[/itex] integer values of

For example, take p = 7. The squares mod 7 are 0, 1, 2, 4, so the quadratic residues mod 7 are 0, 1, 2 and 4. The quadratic non-residues are 3, 5 and 6, because you can't find an integer that squares to give 3, 5 or 6, modulo 7.

- #3

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Thanks but how does one get to the p/2-1/2?

- #4

FeDeX_LaTeX

Gold Member

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There is a nice proof on the first page of this document -- see Proposition 1.2.

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