[JEE Advanced 1983] prove that for any odd positive integer n n n 2 1 is divisible
Prove that for any odd positive integer $n$, $n(n^2-1)$ is divisible by $24$.
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✓ Vidaara Team
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· 2d ago
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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.
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