From: rwg@sdf.lonestar.org
I thought the appearance of 2s (or 3s ...) in the coefficients of factor(x^n-1) was equivalent to >= three (or four ...)� distinct primes dividing n, but it seems they can't all be 3 mod 4 since n=231 fails.
Phil Carmody> What's "failure"? Height+1 < # distinct odd prime factors of n.
There are cyclotomic polynomials Phi(pqr) with maximum height 1 where p,q,r == 1 (mod 4)
E.g.?
and cyclotomic polynomials with huge maximum height where p,q,r == 3 (mod 4), such as pqr=79.131.199 with height 41.
Phil
Mma 7.0 seems to disagree: Max@@Abs/@CoefficientList[#,x]&/@List@@Factor[x^(79*13*199)-1] {1, 1, 1, 1, 1, 1, 1, 2} (with >10^5 terms in that last factor), whereas Max@@Abs/@CoefficientList[#,x]&/@List@@Factor[x^(3*5*7*11)-1] {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 3, 3} --rwg HETEROPYCNOSIS HYPOSECRETIONS