Let $k \geq 2$ be a positive integer and let $n=2^k+1$. How can I prove that $n$ is a prime number if and only if $$3^{\frac{n-1}{2}} \equiv -1 \pmod n.$$
Fixed.
Let $k \geq 2$ be a positive integer and let $n=2^k+1$. How can I prove that $n$ is a prime number if and only if $$3^{\frac{n-1}{2}} \equiv -1 \pmod n.$$
Fixed.