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Show that n3-n is divisible by 6

Answer» Since, it is divisible by both 2 and 3 . So, it must be divisible by 6..
Also, (n-1) , n and (n+1) are 3 consecutive integers thus as proved n3-n must be divisible by 3..
Now, out of three (n-1) , n and (n+1) , one must be divisible by 2..
n3-n => n(n2 - 1) => n (n-1)(n+1) ..


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