https://meashiri.github.io/ctf-writeups/posts/202312-backdoorctf/#something-in-common
TLDR: This is a classic broadcast attack with the same message with a small e (e=3) and different modulii. However, the wrinkle is that the moduli are **NOT Co-prime** to each other.  We can use the CRT() method in Sagemath or Sympy, which addresses this edge case. 