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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- Apr 15th 2012, 09:24 AMalexandrabel90quadratic 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? - Apr 15th 2012, 01:42 PMa tutorRe: 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.

$\displaystyle x_i^2\equiv x_j^2 \mod p \Rightarrow (x_i-x_j)(x_i+x_j)\equiv 0 \mod p$ - Apr 16th 2012, 03:22 AMSylvia104Re: Quadratic residues
It may help to know that the set of all quadratic residues $\displaystyle \mod p$ is a subgroup of index $\displaystyle 2$ of $\displaystyle \mathbb Z_p^\times,$ the multiplicative group of the integers $\displaystyle \mod p.$ 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.