There was nothing deep or mysterious for me. I took the modulus 127
from Fabrizio's post. I did not try to think about what it means.
Perhaps you can explain that.
-sen
On Mon, 12 Feb 2007, Stavros Macrakis wrote:
> On 2/12/07, sen1 at math.msu.edu <sen1 at math.msu.edu> wrote:
>>
>> Note, in my last post, I did not check to see if -56 is really a root.
>>
>> In trying to check it, one gets real nonsense.
>>
>> (%i6) subst(x=-56, x^51+x^22+1);
>> (%o6) -
>> 1437438846217273045233591279433697587696887228686919480393652546754508\
>> 87538187253915320319
>
>
> That's because you weren't calculating with modulus 197 (which only happens
> in the rat package).
>
> modulus:197$
> ratsubst(-56,x,x^51+x^22+1) => 36
>
>
> On the other hand,
>>
>> (%i17) modulus: 127;
>> (%o17) 127
>> (%i18) polymod(x^51+x^22+1);
>> 51 22
>> (%o18) x + x + 1
>> (%i19) factor(%)$
>>
>> (%i20) p(u):= subst(x=u,factor(%o18));
>> (%o20) p(u) := subst(x = u, factor(%o18))
>> (%i21) p(-56);
>> (%o21) 0
>> (%i22)
>>
>> So, it seemed to find the root symbolically.
>>
>
> Sorry, I don't understand the relevance of the mod 127 result for mod 197.
> Is this a typo, or some deep mathematical connection that's eluding me?
>
> -s
>