What would mortgage payments be if monthly payments were constant in real terms?
Note most of the argumentation adapts off the standard derivation for constant nominal payments from Wikipedia.

Let us assume $c$ is a yearly payment for the sake of simplicity. Consider how much is left to be repaid after each year. The principal remaining after the first year is $P_1=(1+r)P-c$. That is, the initial amount plus interest less the payment. After the second year $P_2=(1+r) P_1 - c$ is left, so $P_2=(1+r)((1+r)P-c)-c(1+\pi)$. Note we need to pay $c(1+\pi)$ instead of $c$ so that we are still paying $c$ in real terms for the second year. If the whole loan was repaid after two years, $P_2=0$, so $P = \frac{c}{1+r}+\frac{c(1+\pi)}{(1+r)^2}$.

This equation generalizes for a term of $n$ years, $$P = \frac{c}{1+r} \sum_{k=0}^{n-1} \frac{(1+\pi)^k}{(1+r)^k}$$. This is a geometric series which has the sum
$P=\frac{c}{1+r}\left(\frac{1-\frac{1+\pi}{1+r}^n}{1-\frac{1+\pi}{1+r}}\right)$
which can be rearranged to give $$c=\frac{P(1+r)}{\left(\frac{1-\frac{1+\pi}{1+r}^n}{1-\frac{1+\pi}{1+r}}\right)}$$. The nominal payment for year $n$ will be $c(1+\pi)^{(n-1)}$.