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

Laël Cellier <[email protected]> Sat, 28 Mar 2026 08:33:01 +0100
Newsgroups	gmane.comp.mathematics.pari.user
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    <pre>On Fri, Mar 27, 2026 at 02:26:49PM +0100, La=C3=ABl Cellier wrot=
e:
&gt; Bonjour,
&gt;=20
&gt; if I have a finite field factorization which too complex to be compu=
te
&gt; automatically. For example, let s say
&gt; 21888242871839275222246405745257275088696311157297823662689037894645=
226208583=C2=B9=C2=B2=E2=88=921=3D2
&gt; =C3=97 2 =C3=97 2 =C3=97 2 =C3=97 2 =C3=97 3 =C3=97 3 =C3=97 3 =C3=97=
 5 =C3=97 7 =C3=97 11 =C3=97 13 =C3=97 17 =C3=97 29 =C3=97 67 =C3=97 163 =
=C3=97 229 =C3=97
&gt; 311 =C3=97 397 =C3=97 983 =C3=97 3769 =C3=97 4051 =C3=97 11003 =C3=97=
 43913 =C3=97 1400587 =C3=97 5830087 =C3=97
&gt; 32159167 =C3=97 405928799 =C3=97 11465965001 =C3=97 41692944763 =C3=97=
 152001576931 =C3=97
&gt; 52920684769483 =C3=97 3005054907817151659 =C3=97 3388996819669187238=
034903 =C3=97
&gt; 13427688667394608761327070753331941386769 =C3=97
&gt; 104348903484733242407804502753091803656481823949 =C3=97
&gt; 64146966983547661987959683617937708319359041535057415875983506058816=
159059153647304344187619
&gt; =C3=97 292709098791663788479256587 =C3=97 12051215992189917705435977=
48775484291 =C3=97
&gt; 1299287670584980812472075235801753046609485536283861463811601644579 =
=C3=97
&gt; 64177052757608003316984792821190393947290473614419530386479121451917=
6411228054183938350095736674349376893928388904130308238154900049143893669=
96109
&gt; =C3=97 493356762637 =C3=97 493356762637 =C3=97 212643728920758595086=
1 =C3=97
&gt; 99958339237566847387819651978153731703086441622746320518140724932023=
9784466025001570156606898657304482428213741734451272417306338613370083558=
4740751075324811175115719549874430103358645783161654857
&gt;=20
&gt; Then, how can I provide such a factorization to Pari/gp in order to =
compute
&gt; arbitrary nth roots? I m meaning, doing the reverse of Modexp.

The simplest way is to use addprimes on all primes factors larger than 2^=
28.

Cheers,
Bill






Hi, but what do you mean=E2=80=AF? Using addprimes with which functions=E2=
=80=AF?
Cordialement,</pre>
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