[math-fun] Divisors of polynomials

Playing around with the cyclotomic polynomial P(n) = n^2 + n + 1 I noticed that there are many primes that cannot divide this quantity for any n (e.g., 5, 11). I suppose this is probably related to quadratic reciprocity. Can it be determined just which primes can't divide n^2 + n + 1 for any n ? What about other polynomials, cyclotomic and otherwise? --Dan E.g.: For 5, the residues of P(n) are 1,-2 (twice each) and 2 (once). For 11, the residues of P(n) are 1,2,3,-1,-4 (twice each) and -2 (once). Why these funny patterns? _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele