Let $G=\{n \in \Bbb N \mid n\leq 55 , \; \gcd(n,55)=1\}$ be the group under multiplication modulo $55$. Find $x$ is $x^2=26$ and $x>30$
How many solutions of $\mod 63$ : $x^2=1 \pmod7 $ and $x^3=1\pmod 9$