Find the largest number, which exactly divides every number of the form (n³ - n) (n - 2) where n is a natural number greater than 2.

Solution (By Examveda Team)

$$\eqalign{ & \Rightarrow \left( {{n^3} - n} \right)\left( {n - 2} \right){\text{put n = 3}} \cr & \Rightarrow \left( {{3^3} - 3} \right)\left( {3 - 2} \right) \cr & \Rightarrow \left( {27 - 3} \right) \times 1 \cr & \Rightarrow 24 \cr & {\text{It is divisible by }}24 \cr} $$