Bobosharif S. answered • 04/17/18

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For n=1, we have 1-1=0, 0 is divisible by 3.

Assume that this is true for n and we have to show that its true for n+1

(n+1)

^{3}-(n+1)=n^{3}+3n^{2}+2n=n^{3}-n+3(n^{2}+n) is divisible by 3; n^{3}-n by 3 by is divisible by assumption and 3(n^{2}+n) is divisible as well. So, if n3-n is divisible by 3, then (n+1)^{3}-(n+1) is divisible as well.