## Cyclotomic polynomials' factors - the second coming...

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• I m curious if there s anything special about the factors of cyclotomic polynomials which are also factors of smaller cyclotomics. e.g. 67 | Phi(1474, 3) but
Message 1 of 2 , Dec 25, 2002
I'm curious if there's anything special about the factors of cyclotomic
polynomials which are also factors of smaller cyclotomics.

e.g.
67 | Phi(1474, 3)
but
67 | Phi(22, 3) first.

These repeated factors do not have the same properties as the primitive
factors (not ==1 modulo the exponent).

Is there anything special about them, or are they merely chaff that gets
discarded as uninteresting, or an annoyace?

Phil

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• ... I m curious if there s anything special about the ... I have also looked at these factors.. It seems and this is only a conjecture that Let a1
Message 2 of 2 , Jan 2, 2003
--- Phil Carmody <thefatphil@...> wrote: >
I'm curious if there's anything special about the
> factors of cyclotomic
> polynomials which are also factors of smaller
> cyclotomics.
>
> e.g.
> 67 | Phi(1474, 3)
> but
> 67 | Phi(22, 3) first.
>
> These repeated factors do not have the same
> properties as the primitive
> factors (not ==1 modulo the exponent).
>
> Is there anything special about them, or are they
> merely chaff that gets
> discarded as uninteresting, or an annoyace?
>
> Phil
>
>
I have also looked at these factors..
It seems and this is only a conjecture that
Let a1<a2
then if p|a1
p|a2 => a2=p*a1. (note <= is not true)
A few examples

17|phi(272,7) and 17|phi(16,7) also 16*17=272
113|phi(1582,7) and 113|phi(14,7) also 14*113=1582
59|phi(1711,7) and 59|phi(29,7) also 29*59=1711
5|phi(2500,7) and 5|phi(500,7) also 5*500=2500
109|phi(2943,7) and 109|(27,7) also 27*109=2943

Gary

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