Using mathematical induction prove that 
is divisible by 3.
= 3.n
p(1) : = 1-1=0 =3.0 is divisible by 3
LET p(k) := (k3 - k) =3.k is divisible by 3.
we have to find
p(k+1) := ( (k+1)3 -( k+1) ) is divisible by 3.
p(k+1) := ( k3 + 3k2+ 3k+1 - k-1 ) = k3 - k + 3k2+ 3k
= 3k + 3(k2+ k) = 3 . ( k + (k2+ k) ) is always divisible by 3.