Consider the linear congruence equation $nx ≡ b \pmod {n^2}$ where $n ≥ 1$.
Determine the integers $b$ for which there are solutions and state the number of solutions.
For there to be solutions $g = \gcd(n^2, n)=n$ must divide b.
So there are solutions for $b=nk$ for some integer $k$, that is, $b$ is a multiple of $n$.
The number of incongruent solutions is $n$.