Computing Legendre symbol of a (p = prime number raised to prime number) mod p?

Example:

What is the Legendre Symbol $$(\frac{3^{24671}}{105953})$$?

Since ($$\frac{3}{105953}$$) $$= -1$$ and the exponent p = prime = $$24671$$ is odd, would this mean the answer would be -1?

By quadratic reciprocity we have $$\left(\frac{3}{105953}\right)=\left(\frac{105953}{3}\right)=\left(\frac{2}{3}\right)=-1$$, since $$105953\equiv 1\bmod 4$$, and therefore $$\left(\frac{3^p}{105953}\right)=\left(\frac{3}{105953}\right)^p=\left(\frac{2}{3}\right)^p=(-1)^p=-1.$$