Question

For every natural number $n,n(n^2-1)$ is divisible by

• A. $4$
• B. $6$
• C. $10$
• D. None of these

Answer 1

Answer: (B)

$n(n^2-1)=(n-1)(n)(n+1)$ It is product of three consecutive natural numbers, so according to Langrange’s theorem it is divisible by $3!$ i.e., $6$