Question

Prove for any positive integer n that n3 − n is divisible by 3.

Answer 1

likewise

4^3-4=60 and is divisible by 3

and moreover n^3 -n is hence becomes divisible of 3

Answer 2

n3-1=n(n2-1)=n(n-1)(n+1)

here. n-1 ,n ,n+1 are three consecutive numbers

so one of the factor multiple of 3

so n3 -1 is multiple of 3

so it is divisible by 3