MathDB

(a) Prove that [5x]\plus{}[5y] \ge [3x\plus{}y] \plus{} [3y\plus{}x], where

x,y \ge 0

and

denotes the greatest integer

\le u

(e.g., [\sqrt{2}]\equal{}1). (b) Using (a) or otherwise, prove that \frac{(5m)!(5n)!}{m!n!(3m\plus{}n)!(3n\plus{}m)!} is integral for all positive integral

m

and

n

Problem Statement