If m ,   n are any two integers and m   &   n are related as m = n 2 - n , Then the expression m 2 - 2 m is always divisible by

Step-by-step solution

Given, m = n 2 - n m = n n - 1 . m 2 - 2 m = m m - 2 = n n - 1 n 2 - n - 2 = n n - 1 n + 1 n - 2 m 2 - 2 m = n - 2   n - 1 n n + 1 . It is the product of 4 consecutive integers. ∴   m 2 - 2 m must be divisible by 24 .