1{
 2 "cells": [
 3  {
 4   "cell_type": "code",
 5   "execution_count": 1,
 6   "id": "04264893",
 7   "metadata": {},
 8   "outputs": [],
 9   "source": [
10    "r = 7237005577332262213973186563042994240857116359379907606001950938285454250989"
11   ]
12  },
13  {
14   "cell_type": "code",
15   "execution_count": 2,
16   "id": "1603b293",
17   "metadata": {},
18   "outputs": [
19    {
20     "data": {
21      "text/plain": [
22       "2^2 * 3 * 11 * 198211423230930754013084525763697 * 276602624281642239937218680557139826668747"
23      ]
24     },
25     "execution_count": 2,
26     "metadata": {},
27     "output_type": "execute_result"
28    }
29   ],
30   "source": [
31    "factor(r - 1)"
32   ]
33  },
34  {
35   "cell_type": "code",
36   "execution_count": 3,
37   "id": "425ceac7",
38   "metadata": {},
39   "outputs": [
40    {
41     "name": "stdout",
42     "output_type": "stream",
43     "text": [
44      "7237005577332262213973186563042994240857116359379907606001950938285454250988\n",
45      "1570463851528226261927580272323658009530148727742783848239914322803198255651\n",
46      "4908983020090465803374304318106080751443647916949975825112097080460587568629\n",
47      "7119675135705137915307919240607293966034195415655343409829245710729128040338\n",
48      "2975531125133123119648879457563281269120703404158613135195788908093573672641\n"
49     ]
50    }
51   ],
52   "source": [
53    "gen = 2\n",
54    "print(pow(gen, (r - 1) / 2, r))\n",
55    "print(pow(gen, (r - 1) / 3, r))\n",
56    "print(pow(gen, (r - 1) / 11, r))\n",
57    "print(pow(gen, (r - 1) / 198211423230930754013084525763697, r))\n",
58    "print(pow(gen, (r - 1) / 276602624281642239937218680557139826668747, r))"
59   ]
60  },
61  {
62   "cell_type": "code",
63   "execution_count": null,
64   "id": "f4c58ca4",
65   "metadata": {},
66   "outputs": [],
67   "source": []
68  }
69 ],
70 "metadata": {
71  "kernelspec": {
72   "display_name": "SageMath 9.2",
73   "language": "sage",
74   "name": "sagemath"
75  },
76  "language_info": {
77   "codemirror_mode": {
78    "name": "ipython",
79    "version": 3
80   },
81   "file_extension": ".py",
82   "mimetype": "text/x-python",
83   "name": "python",
84   "nbconvert_exporter": "python",
85   "pygments_lexer": "ipython3",
86   "version": "3.9.7"
87  }
88 },
89 "nbformat": 4,
90 "nbformat_minor": 5
91}