--- On Sun, 5/10/09, math-fun-request@mailman.xmission.com <math-fun-request@mailman.xmission.com> wrote:

...

There are cyclotomic polynomials Phi(pqr) with maximum height 1 where p,q,r == 1 (mod 4)

E.g.?

p = 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000949 q = 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000004533 r = 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000949000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000045330000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000004301816 Using what appears to be one Nathan Kaplan's 2007 result on flat cyclotomics, namely: if p<q<r are prime, and r == +/-1 mod pq, then Phi(pqr) is flat. Note, this is an _if_, not an _iff_. There are interesting flat cases that cannot be proved this way. I might investigate these depending on whether I can steal a copy of Kaplan's paper from somewhere. Phil