## Re: Xmas puzzle

Expand Messages
• ... at X=59448^1801 ... has the (monic, ... the real part of ... I don t know much about number fields, so I can t say that it isn t relevant. Winding things
Message 1 of 3 , Dec 30, 2005
mikeoakes2@... wrote:
><ratwain@...> writes:
>
>>154275005845*59448^14408-3488484120*59448^12607+90930840*59448^10806+9177840*59448^9005-82990*59448^7204+16680*59448^5403+1
>
>This is the value of the polynomial
>P(X)=154275005845*X^8-3488484120*X^7+90930840*X^6+9177840*X^5-82990*X^4+16680*X^3+1;
at X=59448^1801
>
>According to PariGP, the number field defined by P(X)
has the (monic,
>simpler, irreducible) defining polynomial:
>p(X)=x^8-4*x^7+77*x^6-217*x^5+1750*x^4-3143*x^3+12692*x^2-11156*x+23281
>
>And the polynomial p(X) has 4 pairs of complex roots,
the real part of
>each being [amazingly enough] precisely 1/2.
>
>Is this relevant, I wonder...?

I don't know much about number fields, so I can't say
that it isn't relevant.

Winding things up in time for the new year: the