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

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- May 30th 2009, 08:47 AMsidiroots
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 - May 30th 2009, 11:40 AMNonCommAlg
actually there's no solution! (Nod) 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. - May 30th 2009, 03:31 PMputnam120
Oh whoops totally forgot about that. I'll remove the previous post.