Question 15
Let $M$ and $N$ be non-negative integers such that $C_{1010}^{2021}$ is divisible by $2^M\times3^N$. Find the sum of all the possible values of $M+N$. (Note: $C_{1010}^{2021}$ refers to the combination of $2021$ things taken $1010$ at a time without repetition.) Show your detailed solution.