232 | 20^n + 16^n - 3^n - 1

Problem:
If $n$ is even, then $323 | 20^n + 16^n - 3^n - 1$.

Solution:
Let $n = 2k$.
We have $17 | 400^k - 9^k$ and $17 | 256^k - 1$. Hence $17 | 20^n + 16^n - 3^n - 1$.
Also $19 | 20^n -1$ and $19 | 256^k - 9^k$. Hence  $19 | 20^n + 16^n - 3^n - 1$.
Hence it is divisible by $17 \times 19 = 323$. QED