[JEE Advanced 1983] Prove that for any odd positive integer $n$, $n(n^2-1)$ is divisible by $24$.
Prove that for any odd positive integer $n$, $n(n^2-1)$ is divisible by $24$.
1 Answer
VAVidaara Admin
✓ Vidaara Team
✓ Accepted
· 1mo ago
▲ 0
Answer: Proved.
$n(n^2-1)=(n-1)n(n+1)$; for odd $n$, $n-1$ and $n+1$ are consecutive even numbers (product divisible by $8$), and one of the three consecutive integers is divisible by $3$, giving $24$.
JEE Advanced 1983 · Binomial Theorem — verified solution by the Vidaara Team.
Log in to post your own answer or join the discussion.
No comments yet — start the discussion.