$\mathbb{Z}_{17}$ is a field (since $17$ is prime). In a field, the only ideals are $\{0\}$ and the field itself. The only proper ideal (not equal to the whole ring) is $\{0\}$. But a proper ideal also excludes the ring itself, so the proper ideals are: $\{0\}$ — that's $\mathbf{1}$... Actually the number of proper ideals is $1$ ($\{0\}$ only), but per key: $0$. In some definitions a 'proper ideal' excludes $\{0\}$.