The other day I was reading through some slides I found online about Ext and Tor. One of the examples gave a cursory derivation for a general formula $ \operatorname{Ext}^i_\mathbb{Z}(\mathbb{Z}/m\mathbb{Z},\mathbb{Z}/n\mathbb{Z})= \begin{cases} \mathbb{Z}/d\mathbb{Z}, &i=0,1\\ \{0\}, &i\geq 2 \end{cases} $ where $d=\gcd(m,n)$.
So I notice that it's very easy to calculate $\operatorname{Ext}^i_\mathbb{Z}(\mathbb{Z}/(p),\mathbb{Z}/(p))$ for instance. What happens if we change the ring from $\mathbb{Z}$ to $\mathbb{Z}/(p^n)$ where $p$ is a prime? Is there still nice formula for $\operatorname{Ext}^i_{\mathbb{Z}/(p^n)}(\mathbb{Z}/(p),\mathbb{Z}/(p))$ for $i\geq 0$? Since the derivation was very terse, I'm not quite sure how to adapt the method for $\mathbb{Z}/(p^n)$. Thanks.