Question on cyclotomic polynomials

[franktaw at netscape.net]

Sorry, the word "odd" got left out; that should have been "at least 3 distinct odd prime factors".  However, 231 is still an exception.
 
This still leaves the second question: can you ever have Phi_n having a coefficient that is 2 or larger (in absolute value), while Phi_{k*n} does not?  A quick look at A117318 and A117223 suggests that it is not, but this is not definitive.
 
Franklin T. Adams-Watters
 
-----Original Message-----
From: Edwin Clark eclark at math.usf.edu

On Fri, 19 May 2006 franktaw at netscape.net wrote:

> Somebody on this list must know the answer to this question.
>  
> It is well known that the cyclomatic polynomial Phi_n of order n can have a 
coefficient with absolute value greater than 1 only if n has at least 3 distinct 
prime factors.  The question is, is this if and only if?
>  

No, if n = 2*3*5 or 3*7*11 then Phi_n(x) has coefficients 0,1,-1 only. 

Maple calculates Phi_n(x) for such values of n pretty fast.
___________________________________________________
Try the New Netscape Mail Today!
Virtually Spam-Free | More Storage | Import Your Contact List
http://mail.netscape.com
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://list.seqfan.eu/pipermail/seqfan/attachments/20060519/20f28443/attachment-0001.htm>