I've been thinking about this for some time. Now I'm coming on here in the hope of getting some help; Prove that an+3 + (a + 1)2n+3 is divisible by a2 + a + 1. I can't quite remember the restrictions on n, though I'd imagine it'd be "for all real n ≥ -1" or something similar. Thanks in advance! :) EDIT: The way to do this would probably be through the method of mathematical induction, since that was the subject of class the day this problem was given.