How many roots has the polynomial $\displaystyle x^2 - 5 $ v $\displaystyle Z
257?$
I know it can be 0,1 or 2.
thank you
actually there's no solution! applying QRT gives us: $\displaystyle \left(\frac{5}{257} \right)=\left(\frac{257}{5} \right)=\left(\frac{2}{5} \right)=-\left(\frac{5}{2} \right)=-\left(\frac{1}{2} \right)=-1.$
by the way, questions like this one should be posted in the number theory subforum.