(a) Prove that \[ [5x]+[5y] \ge [3x+y] + [3y+x],\] where $ x,y \ge 0$ and $ [u]$ denotes the greatest integer $ \le u$ (e.g., $ [\sqrt{2}]=1$). (b) Using (a) or otherwise, prove that \[ \frac{(5m)!(5n)!}{m!n!(3m+n)!(3n+m)!}\] is integral for all positive integral $ m$ and $ n$.