9 May
2009
9 May
'09
1:23 a.m.
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.
What's "failure"? There are cyclotomic polynomials Phi(pqr) with maximum height 1 where p,q,r == 1 (mod 4) and cyclotomic polynomials with huge maximum height where p,q,r == 3 (mod 4), such as pqr=79.131.199 with height 41. Phil