--- In

primenumbers@yahoogroups.com, Phil Carmody <thefatphil@...>

>wrote:>

> Phi's are cyclotomic polynomials. They are the primitive parts of

the family of

> polynomials f(x) = x^n-1. Equivalently they are the minimal

polynomial which

> vanishes at each of the primitive n-th roots of unity.

> e.g.

> Phi(2) = x+1, as -1 is the only primitive 2nd root of unity,

> Phi(4) = x^2+1, as +/-i are the only two primitive 4th roots of

>unity.

Thank you Phil, Jose and Jack for shedding some light on the theory

and showing some pretty brilliant methodologies to boot. And showing

the capabilities of GP Pari. I have alot to mull over.

Robert, k^n-k^(n-1) has of course factors of k so I assume you did a

typo somewhere?

Mark