Number Theory congruence classes if $n=p^2$ ($p$ is prime)
if $[x]=[1]\mod p$,
Then What is $[x]$ in$\mod n$?
i.e. $[x]=[?]\mod n$
where [x] belongs to (Zn)*
where (Zn)* = {[x] belonging to Zn such that gcd(x.n)=1)

All we can say is that $x\equiv 1+kp\pmod{p^2}$ for some $k$ with $0\le k\le p-1$.
So the congruence class $[x]$ of $x$ modulo $p^2$ can be any one of the $[1+kp]$.
