Question on cyclotomic polynomials

franktaw at netscape.net franktaw at netscape.net
Fri May 19 18:05:12 CEST 2006


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?
 
If the answer to the previous question is no (or unknown), the second question is, is it possible for Phi_n to have such a coefficient, but Phi_{kn} for some k>1 to have only 0's and 1's?
 
Franklin T. Adams-Watters
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