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Show that n3-n is divisible by …

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Show that n3-n is divisible by 6

Posted by Parul Goyal 5 years, 11 months ago

CBSE > Class 10 > Mathematics

4 answers

Aadya Singh ? 5 years, 11 months ago

Since, it is divisible by both 2 and 3 . So, it must be divisible by 6..

Aadya Singh ? 5 years, 11 months ago

Also, (n-1) , n and (n+1) are 3 consecutive integers thus as proved n³-n must be divisible by 3..

Aadya Singh ? 5 years, 11 months ago

Now, out of three (n-1) , n and (n+1) , one must be divisible by 2..

Aadya Singh ? 5 years, 11 months ago

n³-n => n(n² - 1) => n (n-1)(n+1) ..

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