<s>[INST] Integrality of $\frac{n}{3} + \frac{n^2}{2} + \frac{n^3}{6}$ I've been asked to provide a proof for

If $n$ is an integer then
$$\frac{n}{3} + \frac{n^2}{2} + \frac{n^3}{6}$$
is also an integer.

Any help would be appreciated
 [/INST] Hint:$$\frac{n}{6}(n^2+3n+2)=\frac{n}{6}(n+1)(n+2)$$
What can you say about the divisibility of $n,(n+1),(n+2)$ by $2$ and $3$?
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