Prove that for any n [tex]\in[/tex] Z+, the integer (n(n+1)(n+2) + 21) is divisible by 3
A previously proved lemma (see below)
The Attempt at a Solution
I sort of just need a nudge here. I have a previously proven lemma which states:
If d|a and d|b, then d|(a+b)
So armed with this I see that obviously 3|21 and all that remains is to prove n(n+1)(n+2) is divisible by 3. I have tried expanding, which didn't seem to help.