Re: How to compute a finite field nth root using a provided factorization?

Bonjour,

yes, but then, how do I ask Pari to find a nth root=E2=80=AF?

I need to say that I don=E2=80=99t know how to do this when factoring is =
easy=E2=80=A6

Cordialement,

Le 28/03/2026 =C3=A0 08:50, [email protected] a =C3=A9crit=C2=A0=
:
> On 2026-03-28 08:33, La=C3=ABl Cellier wrote:
>>
>> Hi, but what do you mean=E2=80=AF? Using addprimes with which function=
s=E2=80=AF?
>> Cordialement,
>>
>
> ?=20
> n=3D2188824287183927522224640574525727508869631115729782366268903789464=
5226208583^12-1;
> ? #digits(n)
> 917
> ? 2^28
> 268435456
> ? ?addprimes
> addprimes({x=3D[]}): add primes in the vector x to the prime table to b=
e=20
> used in
> trial division. x may also be a single integer. Composite "primes" are=20
> NOT
> allowed.
>
> ? addprimes([405928799 , 11465965001 , 41692944763 , 152001576931 ,=20
> 52920684769483 , 3005054907817151659 , 3388996819669187238034903 ,=20
> 13427688667394608761327070753331941386769 ,=20
> 104348903484733242407804502753091803656481823949 ,=20
> 64146966983547661987959683617937708319359041535057415875983506058816159=
059153647304344187619=20
> , 292709098791663788479256587 , 1205121599218991770543597748775484291=20
> , 1299287670584980812472075235801753046609485536283861463811601644579=20
> ,=20
> 64177052757608003316984792821190393947290473614419530386479121451917641=
1228054183938350095736674349376893928388904130308238154900049143893669961=
09=20
> , 493356762637 , 493356762637 , 2126437289207585950861 ,=20
> 99958339237566847387819651978153731703086441622746320518140724932023978=
4466025001570156606898657304482428213741734451272417306338613370083558474=
0751075324811175115719549874430103358645783161654857]);
> ?
> ? print(factorint(n))
> [2, 5; 3, 3; 5, 1; 7, 1; 11, 1; 13, 1; 17, 1; 29, 1; 67, 1; 163, 1;=20
> 229, 1; 311, 1; 397, 1; 983, 1; 3769, 1; 4051, 1; 11003, 1; 43913, 1;=20
> 1400587, 1; 5830087, 1; 32159167, 1; 405928799, 1; 11465965001, 1;=20
> 41692944763, 1; 152001576931, 1; 493356762637, 1; 52920684769483, 1;=20
> 3005054907817151659, 1; 2126437289207585950861, 1;=20
> 3388996819669187238034903, 1; 292709098791663788479256587, 1;=20
> 1205121599218991770543597748775484291, 1;=20
> 13427688667394608761327070753331941386769, 1;=20
> 104348903484733242407804502753091803656481823949, 1;=20
> 1299287670584980812472075235801753046609485536283861463811601644579,=20
> 1;=20
> 21888242871839275222246405745257275088548364400416034343698204186575808=
495617,=20
> 1;=20
> 64146966983547661987959683617937708319359041535057415875983506058816159=
059153647304344187619,=20
> 1;=20
> 64177052757608003316984792821190393947290473614419530386479121451917641=
1228054183938350095736674349376893928388904130308238154900049143893669961=
09,=20
> 1;=20
> 99958339237566847387819651978153731703086441622746320518140724932023978=
4466025001570156606898657304482428213741734451272417306338613370083558474=
0751075324811175115719549874430103358645783161654857,=20
> 1]
> ? ##
> =C2=A0 ***=C2=A0=C2=A0 last result: cpu time 1 ms, real time 1 ms.
> ?
>
> Regards,
>
> Hermann.