Evaluate $\left(\frac{3}{11}\right)$ using Euler's Criterion.
So far I have:
$$\left(\frac{a}{p}\right) =a^{\frac{p-1}{2}}\implies \left(\frac{3}{11}\right)=3^{\frac{11-1}{2}}=3^5$$
I am a bit lost from here, any help is appreciated, from my understanding the answer should be $\pm 1$ but I do not understand how to arrive at that.
Euler's criterion is used in a prime modulus $p$.
So, if $a\in U_p$, and $a^{(p-1)/2}\equiv 1$ mod $p$, then $\exists x\in U_p$ such that $x^2=a$ (a quadratic residue). If it is -1, then there is no such $x\in U_p$.