$\displaystyle For \ x \in R $ , let [x] be the largest integer less than or equal to x . prove that :$\displaystyle [x] +[x+ \frac{1}{m}]+[x+\frac{2}{m}+[x+\frac{m-1}{m}] =[mx], \forall x \in R , \ \forall m \in N $