Cyclotomic polynomials' factors - the second coming...
- I'm curious if there's anything special about the factors of cyclotomic
polynomials which are also factors of smaller cyclotomics.
67 | Phi(1474, 3)
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?
I Pledge Allegiance to the flag
That appears on my Desktop Startup Screen.
And to the Monopoly for which it Stands:
One Operating System over all, inescapable,
With Freedom and Privacy for none. -- Telecommando on /.
Do you Yahoo!?
Yahoo! Mail Plus - Powerful. Affordable. Sign up now.
- --- Phil Carmody <thefatphil@...> wrote: >
I'm curious if there's anything special about the
> factors of cyclotomicI have also looked at these factors..
> polynomials which are also factors of smaller
> 67 | Phi(1474, 3)
> 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?
It seems and this is only a conjecture that
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
Do You Yahoo!?
Everything you'll ever need on one web page
from News and Sport to Email and Music Charts