let 'n' be any odd natural number. Choose the incorrect statement about the number `n(n^(2)-1)`

Options

A. `n(n^(2)-1)`is always divisible by 4
B. `n(n^(2)-1)` is always divisible by 6
C. `n(n^(2)-1)` is always divisible by 24
D. `n(n^(2)-1)` is always divisible by 18

Answer

D

Explanation

`n(n^(2)-1) = (n-1)n(n+1)`
Put n=2m +1, `m in N`
`n(n^(2)-1) = 4m(2m +1) (m+1)`
`P(m): m(2m+1)(m+1)` is divisible by 6
P(1) is true suppose P(k) is true, `k in N`
`rArr P(k+1)` is true
`rArr P(m)` is true for fall all `m in N`