Question

If n is any odd number greater than 1, then n(n^2-1) is:

a. None of these
b. Divisible by 24 always
c. Divisible by 96 always
d. Divisible by 48 always

Answer 1

For any odd number n greater than 1, n(n^2-1) is divisible by 24 always.

Step-by-step explanation:

To determine if the expression n(n^2-1) is divisible by 24, let's factor it:

n(n^2-1) = n(n+1)(n-1)

Since n is an odd number, it can be expressed as 2k+1, where k is an integer. Substituting this value into the expression:

(2k+1)((2k+1)+1)((2k+1)-1) = (2k+1)(2k+2)(2k) = 24k(k+1)(k+1)

Therefore, for any odd number n greater than 1, n(n^2-1) is divisible by 24 always.