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b Find x such that x2 3 mod 1297 You could just try every x

b) Find x such that x^2 3 mod 1297. You could just try every x from 1 to 648 until you find a solution. is there a shorter route) number theory

Solution

205.2837317

since 1297 is a prime no so X = 376 from above table

x (x^2-3)/1297
36 0.99691596
37 1.053199692
38 1.111025443
39 1.170393215
40 1.231303007
41 1.293754819
42 1.357748651
43 1.423284503
44 1.490362375
45 1.558982267
46 1.629144179
47 1.700848111
48 1.774094063
49 1.848882035
50 1.925212028
51 2.00308404
52 2.082498072
53 2.163454125
54 2.245952197
55 2.32999229
56 2.415574402
57 2.502698535
58 2.591364688
59 2.68157286
60 2.773323053
61 2.866615266
62 2.961449499
63 3.057825752
64 3.155744025
65 3.255204318
66 3.356206631
67 3.458750964
68 3.562837317
69 3.66846569
70 3.775636083
71 3.884348497
72 3.99460293
73 4.106399383
74 4.219737857
75 4.33461835
76 4.451040864
77 4.569005397
78 4.688511951
79 4.809560524
80 4.932151118
81 5.056283732
82 5.181958365
83 5.309175019
84 5.437933693
85 5.568234387
86 5.700077101
87 5.833461835
88 5.968388589
89 6.104857363
90 6.242868157
91 6.382420971
92 6.523515806
93 6.66615266
94 6.810331534
95 6.956052429
96 7.103315343
97 7.252120278
98 7.402467232
99 7.554356207
100 7.707787201
101 7.862760216
102 8.019275251
103 8.177332305
104 8.33693138
105 8.498072475
106 8.66075559
107 8.824980725
108 8.99074788
109 9.158057055
110 9.32690825
111 9.497301465
112 9.6692367
113 9.842713955
114 10.01773323
115 10.19429453
116 10.37239784
117 10.55204318
118 10.73323053
119 10.91595991
120 11.1002313
121 11.28604472
122 11.47340015
123 11.66229761
124 11.85273709
125 12.04471858
126 12.2382421
127 12.43330763
128 12.62991519
129 12.82806476
130 13.02775636
131 13.22898998
132 13.43176561
133 13.63608327
134 13.84194295
135 14.04934464
136 14.25828836
137 14.46877409
138 14.68080185
139 14.89437163
140 15.10948342
141 15.32613724
142 15.54433308
143 15.76407093
144 15.98535081
145 16.20817271
146 16.43253662
147 16.65844256
148 16.88589052
149 17.11488049
150 17.34541249
151 17.57748651
152 17.81110254
153 18.0462606
154 18.28296068
155 18.52120278
156 18.76098689
157 19.00231303
158 19.24518119
159 19.48959136
160 19.73554356
161 19.98303778
162 20.23207402
163 20.48265227
164 20.73477255
165 20.98843485
166 21.24363917
167 21.50038551
168 21.75867386
169 22.01850424
170 22.27987664
171 22.54279106
172 22.80724749
173 23.07324595
174 23.34078643
175 23.60986893
176 23.88049345
177 24.15265998
178 24.42636854
179 24.70161912
180 24.97841172
181 25.25674634
182 25.53662298
183 25.81804163
184 26.10100231
185 26.38550501
186 26.67154973
187 26.95913647
188 27.24826523
189 27.53893601
190 27.8311488
191 28.12490362
192 28.42020046
193 28.71703932
194 29.0154202
195 29.3153431
196 29.61680802
197 29.91981496
198 30.22436392
199 30.5304549
200 30.8380879
201 31.14726291
202 31.45797995
203 31.77023901
204 32.08404009
205 32.39938319
206 32.71626831
207 33.03469545
208 33.35466461
209 33.67617579
210 33.99922899
211 34.32382421
212 34.64996145
213 34.97764071
214 35.30686199
215 35.63762529
216 35.96993061
217 36.30377795
218 36.63916731
219 36.97609869
220 37.31457209
221 37.65458751
222 37.99614495
223 38.33924441
224 38.68388589
225 39.03006939
226 39.37779491
227 39.72706245
228 40.07787201
229 40.43022359
230 40.78411719
231 41.13955281
232 41.49653045
233 41.85505012
234 42.2151118
235 42.5767155
236 42.93986122
237 43.30454896
238 43.67077872
239 44.0385505
240 44.4078643
241 44.77872012
242 45.15111796
243 45.52505783
244 45.90053971
245 46.27756361
246 46.65612953
247 47.03623747
248 47.41788743
249 47.80107941
250 48.18581342
251 48.57208944
252 48.95990748
253 49.34926754
254 49.74016962
255 50.13261372
256 50.52659985
257 50.92212799
258 51.31919815
259 51.71781033
260 52.11796453
261 52.51966076
262 52.922899
263 53.32767926
264 53.73400154
265 54.14186584
266 54.55127217
267 54.96222051
268 55.37471087
269 55.78874325
270 56.20431766
271 56.62143408
272 57.04009252
273 57.46029298
274 57.88203547
275 58.30531997
276 58.73014649
277 59.15651503
278 59.5844256
279 60.01387818
280 60.44487278
281 60.87740941
282 61.31148805
283 61.74710871
284 62.1842714
285 62.6229761
286 63.06322282
287 63.50501157
288 63.94834233
289 64.39321511
290 64.83962992
291 65.28758674
292 65.73708558
293 66.18812645
294 66.64070933
295 67.09483423
296 67.55050116
297 68.0077101
298 68.46646106
299 68.92675405
300 69.38858905
301 69.85196608
302 70.31688512
303 70.78334618
304 71.25134927
305 71.72089437
306 72.1919815
307 72.66461064
308 73.1387818
309 73.61449499
310 74.09175019
311 74.57054742
312 75.05088666
313 75.53276793
314 76.01619121
315 76.50115652
316 76.98766384
317 77.47571318
318 77.96530455
319 78.45643793
320 78.94911334
321 79.44333076
322 79.93909021
323 80.43639167
324 80.93523516
325 81.43562066
326 81.93754819
327 82.44101773
328 82.9460293
329 83.45258288
330 83.96067849
331 84.47031611
332 84.98149576
333 85.49421742
334 86.00848111
335 86.52428682
336 87.04163454
337 87.56052429
338 88.08095605
339 88.60292984
340 89.12644564
341 89.65150347
342 90.17810332
343 90.70624518
344 91.23592907
345 91.76715497
346 92.2999229
347 92.83423285
348 93.37008481
349 93.9074788
350 94.4464148
351 94.98689283
352 95.52891288
353 96.07247494
354 96.61757903
355 97.16422513
356 97.71241326
357 98.26214341
358 98.81341557
359 99.36622976
360 99.92058597
361 100.4764842
362 101.0339244
363 101.5929067
364 102.153431
365 102.7154973
366 103.2791056
367 103.844256
368 104.4109483
369 104.9791827
370 105.5489591
371 106.1202776
372 106.693138
373 107.2675405
374 107.843485
375 108.4209715
376 109
377 109.5805705
378 110.1626831
379 110.7463377
380 111.3315343
381 111.9182729
382 112.5065536
383 113.0963763
384 113.6877409
385 114.2806476
386 114.8750964
387 115.4710871
388 116.0686199
389 116.6676947
390 117.2683115
391 117.8704703
392 118.4741712
393 119.079414
394 119.6861989
395 120.2945258
396 120.9043948
397 121.5158057
398 122.1287587
399 122.7432537
400 123.3592907
401 123.9768697
402 124.5959907
403 125.2166538
404 125.8388589
405 126.462606
406 127.0878951
407 127.7147263
408 128.3430995
409 128.9730146
410 129.6044719
411 130.2374711
412 130.8720123
413 131.5080956
414 132.1457209
415 132.7848882
416 133.4255975
417 134.0678489
418 134.7116423
419 135.3569776
420 136.0038551
421 136.6522745
422 137.3022359
423 137.9537394
424 138.6067849
425 139.2613724
426 139.9175019
427 140.5751735
428 141.234387
429 141.8951426
430 142.5574402
431 143.2212799
432 143.8866615
433 144.5535852
434 145.2220509
435 145.8920586
436 146.5636083
437 147.2367001
438 147.9113338
439 148.5875096
440 149.2652274
441 149.9444873
442 150.6252891
443 151.307633
444 151.9915189
445 152.6769468
446 153.3639167
447 154.0524287
448 154.7424827
449 155.4340786
450 156.1272167
451 156.8218967
452 157.5181187
453 158.2158828
454 158.9151889
455 159.616037
456 160.3184271
457 161.0223593
458 161.7278335
459 162.4348497
460 163.1434079
461 163.8535081
462 164.5651503
463 165.2783346
464 165.9930609
465 166.7093292
466 167.4271396
467 168.1464919
468 168.8673863
469 169.5898227
470 170.3138011
471 171.0393215
472 171.766384
473 172.4949884
474 173.2251349
475 173.9568234
476 174.690054
477 175.4248265
478 176.1611411
479 176.8989977
480 177.6383963
481 178.3793369
482 179.1218196
483 179.8658443
484 180.6114109
485 181.3585197
486 182.1071704
487 182.8573631
488 183.6090979
489 184.3623747
490 185.1171935
491 185.8735544
492 186.6314572
493 187.3909021
494 188.151889
495 188.9144179
496 189.6784888
497 190.4441018
498 191.2112567
499 191.9799537
500 192.7501928
501 193.5219738
502 194.2952968
503 195.0701619
504 195.846569
505 196.6245181
506 197.4040093
507 198.1850424
508 198.9676176
509 199.7517348
510 200.537394
511 201.3245952
512 202.1133385
513 202.9036237
514 203.695451
515 204.4888204
516

205.2837317
b) Find x such that x^2 3 mod 1297. You could just try every x from 1 to 648 until you find a solution. is there a shorter route) number theorySolution205.28373
b) Find x such that x^2 3 mod 1297. You could just try every x from 1 to 648 until you find a solution. is there a shorter route) number theorySolution205.28373
b) Find x such that x^2 3 mod 1297. You could just try every x from 1 to 648 until you find a solution. is there a shorter route) number theorySolution205.28373
b) Find x such that x^2 3 mod 1297. You could just try every x from 1 to 648 until you find a solution. is there a shorter route) number theorySolution205.28373
b) Find x such that x^2 3 mod 1297. You could just try every x from 1 to 648 until you find a solution. is there a shorter route) number theorySolution205.28373
b) Find x such that x^2 3 mod 1297. You could just try every x from 1 to 648 until you find a solution. is there a shorter route) number theorySolution205.28373
b) Find x such that x^2 3 mod 1297. You could just try every x from 1 to 648 until you find a solution. is there a shorter route) number theorySolution205.28373
b) Find x such that x^2 3 mod 1297. You could just try every x from 1 to 648 until you find a solution. is there a shorter route) number theorySolution205.28373
b) Find x such that x^2 3 mod 1297. You could just try every x from 1 to 648 until you find a solution. is there a shorter route) number theorySolution205.28373
b) Find x such that x^2 3 mod 1297. You could just try every x from 1 to 648 until you find a solution. is there a shorter route) number theorySolution205.28373
b) Find x such that x^2 3 mod 1297. You could just try every x from 1 to 648 until you find a solution. is there a shorter route) number theorySolution205.28373

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