For $60\mathrm{\%}$ of the score an easy brute force solution was available, trying every $M$ between $0$ and $10000$ and checking whether all given integers give the same remainder when divided by $M$.

For the full score, we need the following deduction: if some two numbers $A$ and $B$ give the same remainder when divided by $C$, then $C$ divides $A-B$. So for an integer $M$ to be part of the output, it must divide the differences between each pair of input numbers. The largest such $M$ is the greatest common divisor of the differences between input numbers. The remaining values of $M$ are all divisors of the largest $M$ (except for $1$).