For any arbitrary integer $a$, prove that $2 \mid a \left( a+1 \right)$ and $3 \mid a \left( a+1 \right) \left( a+2 \right)$
Proving by strong induction that $\forall n \ge 2, \;\forall d \ge 2 : d \mid n(n+1)(n+2)...(n+d-1) $