I am stuck on this problem, and was wondering if anyone could help me out with this. The question is as follows:
Let $n$ be an integer such that $n ≥ 1$. Prove that $6$ divides $n(n + 1)(n + 2)$.
Note: An integer $a$ divides an integer $b$, written $a|b$, if there exists $q ∈ Z$ such that $b = qa$. Alternatively, $a|b$ if dividing $b$ by $a$, $b ÷ a$, results in an integer.
Should I do a proof by induction?
All help/input is appreciated!