Where did I go wrong on computing the legendre symbol $\left(\frac{150}{1009}\right)$.
I know the answer is $1$. For some reason every way I compute this legendre symbol I get $-1$:
$\left(\frac{150}{1009}\right) = -\left(\frac{75}{1009}\right)$ since we take an odd power of $2$ out
$ = -\left(\frac{25}{1009}\right)\cdot\left(\frac{3}{1009}\right)$ by multiplicativity
$= -\left(\frac{3}{1009}\right)$ since $25$ is a perfect square
$= -1$ since $1009 \mod 12$ is $1$ Theorem.
Using a Computer (Maple) I found that $\left(\frac{75}{1009}\right) = 1$. So my mistake must be in the first step.
- What is the formal rule for factoring out powers of $2$?