So I know I need to test $1,2,3,4,5,6.....,34,35,36$, where $ x^4 \equiv 1 ( \mod37)$ Since we are looking for the 4th roots. Using the totient function I found out that $\phi(4)=2,$ so I must find 2 solutions.
I ended up with $ 6 \& 31$. Since $6^4 \equiv 1 (\mod 37) \& 31^4 \equiv 1 (\mod 37)$ but I'm getting stuck since when I calculated $36^4 \equiv 1 (\mod 37)$.
Why am I getting 3 solutions when I'm supposed to be having 2.