tl;dr
RSA with the following details:
- `N = P**8 * Q * R`
- `M` is divisible by P, thus **not** co-prime with `N`
- `E` and `D` are usual RSA parameters: `E = 65537` and `E*D ≡ 1 (mod φ(N))`
- `C = M**E (mod N)` is known
- `D(C) = (M**E)**D (mod N)` is known as well

`M = P**3 * X` and find `P` and `X` separately.

Original writeup (https://github.com/hnn4abo/ctf/tree/master/K3RN3LCTF/non-square-freedom).