Modular Binomials

This problem is the problem I did not manage to solve in NUS Greyhats GreyCTF2022. Although I am pretty close to the solution, there is one trick that I missed that is crucial to this particular type of challenge. 1 2 3 N = p * q c1 = (2 * p + 3 * q) ** e1 mod N c2 = (5 * p + 7 * q) ** e2 mod N We are given the above system of equations, and the goal is to solve for $p$ and $q$....