<HTML><BODY><DIV style='font-family: "Verdana"; font-size: 10pt;'><DIV>
<DIV>Sorry, the word "odd" got left out; that should have been "at least 3 distinct odd prime factors". However, 231 is still an exception.</DIV>
<DIV> </DIV>
<DIV>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.</DIV>
<DIV> </DIV>
<DIV>Franklin T. Adams-Watters<BR> <BR>-----Original Message-----<BR>From: Edwin Clark <A href="mailto:eclark@math.usf.edu">eclark@math.usf.edu</A><BR><TT></TT></DIV>
<DIV><TT>On Fri, 19 May 2006 <A href="mailto:franktaw%40netscape.net">franktaw@netscape.net</A> wrote:<BR><BR>> Somebody on this list must know the answer to this question.<BR>> <BR>> It is well known that the cyclomatic polynomial Phi_n of order n can have a <BR>coefficient with absolute value greater than 1 only if n has at least 3 distinct <BR>prime factors. The question is, is this if and only if?<BR>> <BR><BR>No, if n = 2*3*5 or 3*7*11 then Phi_n(x) has coefficients 0,1,-1 only. <BR><BR>Maple calculates Phi_n(x) for such values of n pretty fast.<BR><BR></DIV></TT><!-- end of AOLMsgPart_0_65ce9b82-1162-4d87-90a6-e182f3b1c5cf --></DIV></DIV>
<hr style="MARGIN-TOP:10px" >
<b>Try the New Netscape Mail Today!</b><br />
Virtually Spam-Free | More Storage | Import Your Contact List<br /><a href="http://mail.netscape.com">http://mail.netscape.com</a>
</BODY></HTML>