--- 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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