Question

for n a natural number prove that if n greater than or equal to 2, then n ^3 - n is always divisible by 3

Answer 1

pls help

Answer 2

n^3-n
=n(n^2-1)
=(n-1)* n *(n+1)

For any natural no ,n one of n, or (n-1), or (n+1) will always be divisible by 3.
So n^3-n will always be divisible 3 for any natural no ,n