cSolutions de l'équation x²-Ny² = 1 (dite de Pell-Fermat) pour 1 < n <= 1000

Solutions trouvées par développement en fraction continue de la racine carrée de n, selon la méthode de Lagrange (1768) avec le logiciel frac1a.exe écrit en Turbo Pascal par Yves Sagnier.
 
n a0 parité de
la période
période x y vérification :
x²-Ny² =
2 1 - impair 1 3 2 1
3 1 - pair 2 2 1 1
4 2

n est un carré

5 2 - impair 1 9 4 1
6 2 - pair 2 5 2 1
7 2 - pair 4 8 3 1
8 2 - pair 2 3 1 1
9 3

n est un carré

10 3 - impair 1 19 6 1
11 3 - pair 2 10 3 1
12 3 - pair 2 7 2 1
13 3 - impair 5 649 180 1
14 3 - pair 4 15 4 1
15 3 - pair 2 4 1 1
16 4

n est un carré

17 4 - impair 1 33 8 1
18 4 - pair 2 17 4 1
19 4 - pair 6 170 39 1
20 4 - pair 2 9 2 1
21 4 - pair 6 55 12 1
22 4 - pair 6 197 42 1
23 4 - pair 4 24 5 1
24 4 - pair 2 5 1 1
25 5

n est un carré

26 5 - impair 1 51 10 1
27 5 - pair 2 26 5 1
28 5 - pair 4 127 24 1
29 5 - impair 5 9801 1820 1
30 5 - pair 2 11 2 1
31 5 - pair 8 1520 273 1
32 5 - pair 4 17 3 1
33 5 - pair 4 23 4 1
34 5 - pair 4 35 6 1
35 5 - pair 2 6 1 1
36 6

n est un carré

37 6 - impair 1 73 12 1
38 6 - pair 2 37 6 1
39 6 - pair 2 25 4 1
40 6 - pair 2 19 3 1
41 6 - impair 3 2049 320 1
42 6 - pair 2 13 2 1
43 6 - pair 10 3482 531 1
44 6 - pair 8 199 30 1
45 6 - pair 6 161 24 1
46 6 - pair 12 24335 3588 1
47 6 - pair 4 48 7 1
48 6 - pair 2 7 1 1
49 7

n est un carré

50 7 - impair 1 99 14 1
51 7 - pair 2 50 7 1
52 7 - pair 6 649 90 1
53 7 - impair 5 66249 9100 1
54 7 - pair 6 485 66 1
55 7 - pair 4 89 12 1
56 7 - pair 2 15 2 1
57 7 - pair 6 151 20 1
58 7 - impair 7 19603 2574 1
59 7 - pair 6 530 69 1
60 7 - pair 4 31 4 1
61 7 - impair 11 1766319049 226153980 1
62 7 - pair 4 63 8 1
63 7 - pair 2 8 1 1
64 8

n est un carré

65 8 - impair 1 129 16 1
66 8 - pair 2 65 8 1
67 8 - pair 10 48842 5967 1
68 8 - pair 2 33 4 1
69 8 - pair 8 7775 936 1
70 8 - pair 6 251 30 1
71 8 - pair 8 3480 413 1
72 8 - pair 2 17 2 1
73 8 - impair 7 2281249 267000 1
74 8 - impair 5 3699 430 1
75 8 - pair 4 26 3 1
76 8 - pair 12 57799 6630 1
77 8 - pair 6 351 40 1
78 8 - pair 4 53 6 1
79 8 - pair 4 80 9 1
80 8 - pair 2 9 1 1
81 9

n est un carré

82 9 - impair 1 163 18 1
83 9 - pair 2 82 9 1
84 9 - pair 2 55 6 1
85 9 - impair 5 285769 30996 1
86 9 - pair 10 10405 1122 1
87 9 - pair 2 28 3 1
88 9 - pair 6 197 21 1
89 9 - impair 5 500001 53000 1
90 9 - pair 2 19 2 1
91 9 - pair 8 1574 165 1
92 9 - pair 8 1151 120 1
93 9 - pair 10 12151 1260 1
94 9 - pair 16 2143295 221064 1
95 9 - pair 4 39 4 1
96 9 - pair 4 49 5 1
97 9 - impair 11 62809633 6377352 1
98 9 - pair 4 99 10 1
99 9 - pair 2 10 1 1
100 10

n est un carré

101 10 - impair 1 201 20 1
102 10 - pair 2 101 10 1
103 10 - pair 12 227528 22419 1
104 10 - pair 2 51 5 1
105 10 - pair 2 41 4 1
106 10 - impair 9 32080051 3115890 1
107 10 - pair 6 962 93 1
108 10 - pair 8 1351 130 1
109 10 - impair 15 158070671986249 15140424455100 1
110 10 - pair 2 21 2 1
111 10 - pair 6 295 28 1
112 10 - pair 6 127 12 1
113 10 - impair 9 1204353 113296 1
114 10 - pair 6 1025 96 1
115 10 - pair 10 1126 105 1
116 10 - pair 10 9801 910 1
117 10 - pair 6 649 60 1
118 10 - pair 10 306917 28254 1
119 10 - pair 4 120 11 1
120 10 - pair 2 11 1 1
121 11

n est un carré

122 11 - impair 1 243 22 1
123 11 - pair 2 122 11 1
124 11 - pair 16 4620799 414960 1
125 11 - impair 5 930249 83204 1
126 11 - pair 4 449 40 1
127 11 - pair 12 4730624 419775 1
128 11 - pair 4 577 51 1
129 11 - pair 10 16855 1484 1
130 11 - impair 3 6499 570 1
131 11 - pair 6 10610 927 1
132 11 - pair 2 23 2 1
133 11 - pair 16 2588599 224460 1
134 11 - pair 14 145925 12606 1
135 11 - pair 8 244 21 1
136 11 - pair 4 35 3 1
137 11 - impair 9 6083073 519712 1
138 11 - pair 4 47 4 1
139 11 - pair 18 77563250 6578829 1
140 11 - pair 4 71 6 1
141 11 - pair 4 95 8 1
142 11 - pair 4 143 12 1
143 11 - pair 2 12 1 1
144 12

n est un carré

145 12 - impair 1 289 24 1
146 12 - pair 2 145 12 1
147 12 - pair 2 97 8 1
148 12 - pair 2 73 6 1
149 12 - impair 9 25801741449 2113761020 1
150 12 - pair 2 49 4 1
151 12 - pair 20 1728148040 140634693 1
152 12 - pair 2 37 3 1
153 12 - pair 8 2177 176 1
154 12 - pair 10 21295 1716 1
155 12 - pair 4 249 20 1
156 12 - pair 2 25 2 1
157 12 - impair 17 46698728731849 3726964292220 1
158 12 - pair 8 7743 616 1
159 12 - pair 10 1324 105 1
160 12 - pair 8 721 57 1
161 12 - pair 10 11775 928 1
162 12 - pair 10 19601 1540 1
163 12 - pair 18 64080026 5019135 1
164 12 - pair 6 2049 160 1
165 12 - pair 6 1079 84 1
166 12 - pair 22 1700902565 132015642 1
167 12 - pair 4 168 13 1
168 12 - pair 2 13 1 1
169 13

n est un carré

170 13 - impair 1 339 26 1
171 13 - pair 2 170 13 1
172 13 - pair 16 24248647 1848942 1
173 13 - impair 5 2499849 190060 1
174 13 - pair 4 1451 110 1
175 13 - pair 6 2024 153 1
176 13 - pair 4 199 15 1
177 13 - pair 8 62423 4692 1
178 13 - pair 6 1601 120 1
179 13 - pair 14 4190210 313191 1
180 13 - pair 4 161 12 1
181 13 - impair 21 2469645423824185801 183567298683461940 1
182 13 - pair 2 27 2 1
183 13 - pair 6 487 36 1
184 13 - pair 12 24335 1794 1
185 13 - impair 5 9249 680 1
186 13 - pair 10 7501 550 1
187 13 - pair 6 1682 123 1
188 13 - pair 8 4607 336 1
189 13 - pair 4 55 4 1
190 13 - pair 14 52021 3774 1
191 13 - pair 16 8994000 650783 1
192 13 - pair 4 97 7 1
193 13 - impair 13 6224323426849 448036604040 1
194 13 - pair 4 195 14 1
195 13 - pair 2 14 1 1
196 14

n est un carré

197 14 - impair 1 393 28 1
198 14 - pair 2 197 14 1
199 14 - pair 20 16266196520 1153080099 1
200 14 - pair 2 99 7 1
201 14 - pair 14 515095 36332 1
202 14 - impair 7 19731763 1388322 1
203 14 - pair 2 57 4 1
204 14 - pair 8 4999 350 1
205 14 - pair 8 39689 2772 1
206 14 - pair 8 59535 4148 1
207 14 - pair 8 1151 80 1
208 14 - pair 6 649 45 1
209 14 - pair 8 46551 3220 1
210 14 - pair 2 29 2 1
211 14 - pair 26 278354373650 19162705353 1
212 14 - pair 14 66249 4550 1
213 14 - pair 12 194399 13320 1
214 14 - pair 26 695359189925 47533775646 1
215 14 - pair 4 44 3 1
216 14 - pair 6 485 33 1
217 14 - pair 16 3844063 260952 1
218 14 - impair 5 126003 8534 1
219 14 - pair 4 74 5 1
220 14 - pair 4 89 6 1
221 14 - pair 6 1665 112 1
222 14 - pair 4 149 10 1
223 14 - pair 4 224 15 1
224 14 - pair 2 15 1 1
225 15

n est un carré

226 15 - impair 1 451 30 1
227 15 - pair 2 226 15 1
228 15 - pair 2 151 10 1
229 15 - impair 5 5848201 386460 1
230 15 - pair 2 91 6 1
231 15 - pair 2 76 5 1
232 15 - pair 6 19603 1287 1
233 15 - impair 11 1072400673 70255304 1
234 15 - pair 8 5201 340 1
235 15 - pair 2 46 3 1
236 15 - pair 12 561799 36570 1
237 15 - pair 10 228151 14820 1
238 15 - pair 8 11663 756 1
239 15 - pair 12 6195120 400729 1
240 15 - pair 2 31 2 1
241 15 - impair 17 10085143557001249 649641205044600 1
242 15 - pair 10 19601 1260 1
243 15 - pair 10 70226 4505 1
244 15 - pair 26 1766319049 113076990 1
245 15 - pair 10 51841 3312 1
246 15 - pair 10 88805 5662 1
247 15 - pair 12 85292 5427 1
248 15 - pair 4 63 4 1
249 15 - pair 16 8553815 542076 1
250 15 - impair 7 39480499 2496966 1
251 15 - pair 14 3674890 231957 1
252 15 - pair 4 127 8 1
253 15 - pair 22 3222617399 202604220 1
254 15 - pair 4 255 16 1
255 15 - pair 2 16 1 1
256 16

n est un carré

257 16 - impair 1 513 32 1
258 16 - pair 2 257 16 1
259 16 - pair 10 847225 52644 1
260 16 - pair 2 129 8 1
261 16 - pair 16 192119201 11891880 1
262 16 - pair 14 104980517 6485718 1
263 16 - pair 12 139128 8579 1
264 16 - pair 2 65 4 1
265 16 - impair 9 73738369 4529712 1
266 16 - pair 4 685 42 1
267 16 - pair 6 2402 147 1
268 16 - pair 20 4771081927 291440214 1
269 16 - impair 3 13449 820 1
270 16 - pair 6 5291 322 1
271 16 - pair 24 115974983600 7044978537 1
272 16 - pair 2 33 2 1
273 16 - pair 6 727 44 1
274 16 - impair 7 3959299 239190 1
275 16 - pair 6 199 12 1
276 16 - pair 12 7775 468 1
277 16 - impair 21 159150073798980475849 9562401173878027020 1
278 16 - pair 6 2501 150 1
279 16 - pair 8 1520 91 1
280 16 - pair 6 251 15 1
281 16 - impair 13 2262200630049 134951575480 1
282 16 - pair 8 2351 140 1
283 16 - pair 18 138274082 8219541 1
284 16 - pair 16 24220799 1437240 1
285 16 - pair 6 2431 144 1
286 16 - pair 10 561835 33222 1
287 16 - pair 4 288 17 1
288 16 - pair 2 17 1 1
289 17

n est un carré

290 17 - impair 1 579 34 1
291 17 - pair 2 290 17 1
292 17 - pair 10 2281249 133500 1
293 17 - impair 5 12320649 719780 1
294 17 - pair 6 4801 280 1
295 17 - pair 12 2024999 117900 1
296 17 - pair 6 3699 215 1
297 17 - pair 10 48599 2820 1
298 17 - impair 11 335473872499 19433479650 1
299 17 - pair 4 415 24 1
300 17 - pair 4 1351 78 1
301 17 - pair 26 5883392537695 339113108232 1
302 17 - pair 16 4276623 246092 1
303 17 - pair 6 2524 145 1
304 17 - pair 12 57799 3315 1
305 17 - pair 4 489 28 1
306 17 - pair 2 35 2 1
307 17 - pair 14 88529282 5052633 1
308 17 - pair 6 351 20 1
309 17 - pair 26 64202725495 3652365444 1
310 17 - pair 16 848719 48204 1
311 17 - pair 16 16883880 957397 1
312 17 - pair 4 53 3 1
313 17 - impair 17 32188120829134849 1819380158564160 1
314 17 - impair 7 392499 22150 1
315 17 - pair 4 71 4 1
316 17 - pair 8 12799 720 1
317 17 - impair 11 248678907849 13967198980 1
318 17 - pair 4 107 6 1
319 17 - pair 14 12901780 722361 1
320 17 - pair 4 161 9 1
321 17 - pair 4 215 12 1
322 17 - pair 4 323 18 1
323 17 - pair 2 18 1 1
324 18

n est un carré

325 18 - impair 1 649 36 1
326 18 - pair 2 325 18 1
327 18 - pair 2 217 12 1
328 18 - pair 2 163 9 1
329 18 - pair 12 2376415 131016 1
330 18 - pair 2 109 6 1
331 18 - pair 34 2785589801443970 153109862634573 1
332 18 - pair 8 13447 738 1
333 18 - pair 2 73 4 1
334 18 - pair 28 63804373719695 3491219999244 1
335 18 - pair 4 604 33 1
336 18 - pair 2 55 3 1
337 18 - impair 19 2063810353129713793 112422913565764752 1
338 18 - impair 5 114243 6214 1
339 18 - pair 10 97970 5321 1
340 18 - pair 14 285769 15498 1
341 18 - pair 14 10626551 575460 1
342 18 - pair 2 37 2 1
343 18 - pair 16 130576328 7050459 1
344 18 - pair 10 10405 561 1
345 18 - pair 10 6761 364 1
346 18 - impair 5 17299 930 1
347 18 - pair 14 641602 34443 1
348 18 - pair 8 1567 84 1
349 18 - impair 7 169648201 9081060 1
350 18 - pair 6 449 24 1
351 18 - pair 12 62425 3332 1
352 18 - pair 8 77617 4137 1
353 18 - impair 15 10157115393 540608704 1
354 18 - pair 10 258065 13716 1
355 18 - pair 12 954809 50676 1
356 18 - pair 14 500001 26500 1
357 18 - pair 6 3401 180 1
358 18 - pair 26 176579805797 9332532726 1
359 18 - pair 4 360 19 1
360 18 - pair 2 19 1 1
361 19

n est un carré

362 19 - impair 1 723 38 1
363 19 - pair 2 362 19 1
364 19 - pair 12 4954951 259710 1
365 19 - impair 5 23915529 1251796 1
366 19 - pair 12 907925 47458 1
367 19 - pair 20 19019995568 992835687 1
368 19 - pair 4 1151 60 1
369 19 - pair 12 8396801 437120 1
370 19 - impair 3 213859 11118 1
371 19 - pair 6 1695 88 1
372 19 - pair 6 12151 630 1
373 19 - impair 5 52387849 2712540 1
374 19 - pair 6 3365 174 1
375 19 - pair 10 15124 781 1
376 19 - pair 16 2143295 110532 1
377 19 - pair 4 233 12 1
378 19 - pair 8 8749 450 1
379 19 - pair 30 12941197220540690 664744650125541 1
380 19 - pair 2 39 2 1
381 19 - pair 6 1015 52 1
382 19 - pair 24 164998439999 8442054600 1
383 19 - pair 8 18768 959 1
384 19 - pair 8 4801 245 1
385 19 - pair 16 95831 4884 1
386 19 - pair 12 111555 5678 1
387 19 - pair 6 3482 177 1
388 19 - pair 14 62809633 3188676 1
389 19 - impair 9 3287049 166660 1
390 19 - pair 4 79 4 1
391 19 - pair 16 7338680 371133 1
392 19 - pair 4 99 5 1
393 19 - pair 20 46437143 2342444 1
394 19 - impair 21 312086396361222451 15722685507826110 1
395 19 - pair 4 159 8 1
396 19 - pair 4 199 10 1
397 19 - impair 21 838721786045180184649 42094239791738433660 1
398 19 - pair 4 399 20 1
399 19 - pair 2 20 1 1
400 20

n est un carré

401 20 - impair 1 801 40 1
402 20 - pair 2 401 20 1
403 20 - pair 10 669878 33369 1
404 20 - pair 2 201 10 1
405 20 - pair 2 161 8 1
406 20 - pair 14 59468095 2951352 1
407 20 - pair 6 2663 132 1
408 20 - pair 2 101 5 1
409 20 - impair 21 25052977273092427986049 1238789998647218582160 1
410 20 - pair 2 81 4 1
411 20 - pair 10 49730 2453 1
412 20 - pair 20 103537981567 5100950232 1
413 20 - pair 8 113399 5580 1
414 20 - pair 8 24335 1196 1
415 20 - pair 16 18412804 903849 1
416 20 - pair 8 5201 255 1
417 20 - pair 18 85322647 4178268 1
418 20 - pair 6 33857 1656 1
419 20 - pair 18 270174970 13198911 1
420 20 - pair 2 41 2 1
421 20 - impair 37 3879474045914926879468217167061449 189073995951839020880499780706260 1
422 20 - pair 14 7022501 341850 1
423 20 - pair 8 4607 224 1
424 20 - pair 18 32080051 1557945 1
425 20 - impair 7 143649 6968 1
426 20 - pair 12 88751 4300 1
427 20 - pair 4 62 3 1
428 20 - pair 12 1850887 89466 1
429 20 - pair 12 1524095 73584 1
430 20 - pair 14 2862251 138030 1
431 20 - pair 16 151560720 7300423 1
432 20 - pair 8 1351 65 1
433 20 - impair 21 104564907854286695713 5025068784834899736 1
434 20 - pair 4 125 6 1
435 20 - pair 4 146 7 1
436 20 - pair 30 158070671986249 7570212227550 1
437 20 - pair 6 4599 220 1
438 20 - pair 4 293 14 1
439 20 - pair 4 440 21 1
440 20 - pair 2 21 1 1
441 21

n est un carré

442 21 - impair 1 883 42 1
443 21 - pair 2 442 21 1
444 21 - pair 2 295 14 1
445 21 - impair 5 43468489 2060604 1
446 21 - pair 16 110166015 5216512 1
447 21 - pair 2 148 7 1
448 21 - pair 2 127 6 1
449 21 - impair 17 71798771299708449 3388393513402120 1
450 21 - pair 8 19601 924 1
451 21 - pair 10 46471490 2188257 1
452 21 - pair 10 1204353 56648 1
453 21 - pair 10 1653751 77700 1
454 21 - pair 34 16916040084175685 793909098494766 1
455 21 - pair 2 64 3 1
456 21 - pair 6 1025 48 1
457 21 - impair 25 6983244756398928218113 326662411570389853632 1
458 21 - impair 3 22899 1070 1
459 21 - pair 10 499850 23331 1
460 21 - pair 12 2535751 118230 1
461 21 - impair 15 1182351890184201 55067617520620 1
462 21 - pair 2 43 2 1
463 21 - pair 32 247512720456368 11502891625161 1
464 21 - pair 10 9801 455 1
465 21 - pair 10 15871 736 1
466 21 - pair 22 938319425 43466808 1
467 21 - pair 14 1625626 75225 1
468 21 - pair 8 649 30 1
469 21 - pair 10 137215 6336 1
470 21 - pair 6 1691 78 1
471 21 - pair 14 7838695 361188 1
472 21 - pair 14 306917 14127 1
473 21 - pair 4 87 4 1
474 21 - pair 14 193549 8890 1
475 21 - pair 10 57799 2652 1
476 21 - pair 8 28799 1320 1
477 21 - pair 20 8777860001 401910600 1
478 21 - pair 36 1617319577991743 73974475657896 1
479 21 - pair 12 2989440 136591 1
480 21 - pair 4 241 11 1
481 21 - impair 13 1859131879201 84769117080 1
482 21 - pair 4 483 22 1
483 21 - pair 2 22 1 1
484 22

n est un carré

485 22 - impair 1 969 44 1
486 22 - pair 2 485 22 1
487 22 - pair 28 51906073840568 2352088722477 1
488 22 - pair 2 243 11 1
489 22 - pair 22 7592629975 343350596 1
490 22 - pair 10 1039681 46968 1
491 22 - pair 22 93628044170 4225374483 1
492 22 - pair 8 29767 1342 1
493 22 - impair 9 935662752649 42140131020 1
494 22 - pair 10 73035 3286 1
495 22 - pair 2 89 4 1
496 22 - pair 16 4620799 207480 1
497 22 - pair 10 1201887 53912 1
498 22 - pair 6 179777 8056 1
499 22 - pair 6 4490 201 1
500 22 - pair 14 930249 41602 1
501 22 - pair 28 11242731902975 502288218432 1
502 22 - pair 14 3832352837 171046278 1
503 22 - pair 8 24648 1099 1
504 22 - pair 4 449 20 1
505 22 - pair 4 809 36 1
506 22 - pair 2 45 2 1
507 22 - pair 6 1351 60 1
508 22 - pair 32 44757606858751 1985797689600 1
509 22 - impair 19 313201220822405001 13882400040814700 1
510 22 - pair 6 271 12 1
511 22 - pair 20 4188548960 185290497 1
512 22 - pair 12 665857 29427 1
513 22 - pair 16 13771351 608020 1
514 22 - pair 6 4625 204 1
515 22 - pair 10 17406 767 1
516 22 - pair 10 16855 742 1
517 22 - pair 22 590968985399 25990786260 1
518 22 - pair 6 2367 104 1
519 22 - pair 18 14851876 651925 1
520 22 - pair 6 6499 285 1
521 22 - impair 19 32961431500035201 1444066532654320 1
522 22 - pair 10 19603 858 1
523 22 - pair 22 81810300626 3577314675 1
524 22 - pair 20 225144199 9835470 1
525 22 - pair 6 6049 264 1
526 22 - pair 40 84056091546952933775 3665019757324295532 1
527 22 - pair 4 528 23 1
528 22 - pair 2 23 1 1
529 23

n est un carré

530 23 - impair 1 1059 46 1
531 23 - pair 2 530 23 1
532 23 - pair 10 2588599 112230 1
533 23 - impair 5 74859849 3242540 1
534 23 - pair 10 3678725 159194 1
535 23 - pair 12 1618804 69987 1
536 23 - pair 10 145925 6303 1
537 23 - pair 20 192349463 8300492 1
538 23 - impair 7 9536081203 411129654 1
539 23 - pair 8 3970 171 1
540 23 - pair 8 119071 5124 1
541 23 - impair 39 3707453360023867028800645599667005001 159395869721270110077187138775196900 1
542 23 - pair 16 4293183 184408 1
543 23 - pair 10 669337 28724 1
544 23 - pair 4 2449 105 1
545 23 - pair 6 1961 84 1
546 23 - pair 6 701 30 1
547 23 - pair 26 160177601264642 6848699678673 1
548 23 - pair 14 6083073 259856 1
549 23 - pair 18 1766319049 75384660 1
550 23 - pair 16 30580901 1303974 1
551 23 - pair 6 8380 357 1
552 23 - pair 2 47 2 1
553 23 - pair 26 624635837407 26562217704 1
554 23 - impair 11 60756099699 2581279330 1
555 23 - pair 8 1814 77 1
556 23 - pair 36 12032115501124999 510275358434250 1
557 23 - impair 5 27849 1180 1
558 23 - pair 12 7937 336 1
559 23 - pair 20 506568295 21425556 1
560 23 - pair 4 71 3 1
561 23 - pair 14 522785 22072 1
562 23 - pair 18 220938497 9319728 1
563 23 - pair 10 68122 2871 1
564 23 - pair 4 95 4 1
565 23 - impair 13 435259412378569 18311501103948 1
566 23 - pair 18 95609285 4018758 1
567 23 - pair 6 2024 85 1
568 23 - pair 4 143 6 1
569 23 - impair 19 16760473211643448449 702635588524014320 1
570 23 - pair 4 191 8 1
571 23 - pair 42 181124355061630786130 7579818350628982587 1
572 23 - pair 4 287 12 1
573 23 - pair 4 383 16 1
574 23 - pair 4 575 24 1
575 23 - pair 2 24 1 1
576 24

n est un carré

577 24 - impair 1 1153 48 1
578 24 - pair 2 577 24 1
579 24 - pair 2 385 16 1
580 24 - pair 2 289 12 1
581 24 - pair 24 152071153975 6308974548 1
582 24 - pair 2 193 8 1
583 24 - pair 10 8429543 349116 1
584 24 - pair 2 145 6 1
585 24 - pair 8 33281 1376 1
586 24 - impair 23 33867877212256207699 1399069112058008310 1
587 24 - pair 14 1907162 78717 1
588 24 - pair 2 97 4 1
589 24 - pair 40 41423166067036218751 1706811823063746000 1
590 24 - pair 6 5781 238 1
591 24 - pair 10 165676 6815 1
592 24 - pair 2 73 3 1
593 24 - impair 13 721517598849 29629176560 1
594 24 - pair 10 1098305 45064 1
595 24 - pair 10 18514 759 1
596 24 - pair 22 25801741449 1056880510 1
597 24 - pair 22 463287093751 18961078500 1
598 24 - pair 10 1574351 64380 1
599 24 - pair 28 24686379794520 1008658133851 1
600 24 - pair 2 49 2 1
601 24 - impair 31 38902815462492318420311478049 1586878942101888360258625080 1
602 24 - pair 6 687 28 1
603 24 - pair 10 48842 1989 1
604 24 - pair 44 5972991296311683199 243037569063951720 1
605 24 - pair 12 930249 37820 1
606 24 - pair 20 42187499 1713750 1
607 24 - pair 24 164076033968 6659640783 1
608 24 - pair 8 2737 111 1
609 24 - pair 12 605695 24544 1
610 24 - impair 9 10323982819 418005846 1
611 24 - pair 14 236926 9585 1
612 24 - pair 8 2177 88 1
613 24 - impair 33 464018873584078278910994299849 18741545784831997880308784340 1
614 24 - pair 26 348291186245 14055888354 1
615 24 - pair 4 124 5 1
616 24 - pair 10 21295 858 1
617 24 - impair 15 3363593612801313 135413180018248 1
618 24 - pair 6 10093 406 1
619 24 - pair 38 517213510553282930 20788566180548739 1
620 24 - pair 4 249 10 1
621 24 - pair 6 7775 312 1
622 24 - pair 20 13804370063 553504812 1
623 24 - pair 4 624 25 1
624 24 - pair 2 25 1 1
625 25

n est un carré

626 25 - impair 1 1251 50 1
627 25 - pair 2 626 25 1
628 25 - pair 26 46698728731849 1863482146110 1
629 25 - impair 5 123245001 4914100 1
630 25 - pair 2 251 10 1
631 25 - pair 48 48961575312998650035560 1949129537575151036427 1
632 25 - pair 4 7743 308 1
633 25 - pair 18 440772247 17519124 1
634 25 - impair 23 8711856945587257031251 345992039259400361250 1
635 25 - pair 2 126 5 1
636 25 - pair 12 3505951 139020 1
637 25 - pair 22 1419278889601 56233877040 1
638 25 - pair 8 42283 1674 1
639 25 - pair 16 24220799 958160 1
640 25 - pair 12 1039681 41097 1
641 25 - impair 21 2609429220845977814049 103066257550962737720 1
642 25 - pair 6 5777 228 1
643 25 - pair 22 1988960193026 78436933185 1
644 25 - pair 10 11775 464 1
645 25 - pair 10 1024001 40320 1
646 25 - pair 4 305 12 1
647 25 - pair 16 120187368 4725053 1
648 25 - pair 6 19601 770 1
649 25 - pair 30 1123593226162199 44104892095380 1
650 25 - pair 2 51 2 1
651 25 - pair 6 1735 68 1
652 25 - pair 36 8212499464321351 321626301297510 1
653 25 - impair 19 10499986568677299849 410896226494013260 1
654 25 - pair 16 8915765 348634 1
655 25 - pair 16 737709209 28824684 1
656 25 - pair 10 2049 80 1
657 25 - pair 18 2281249 89000 1
658 25 - pair 8 1693 66 1
659 25 - pair 6 5930 231 1
660 25 - pair 6 1079 42 1
661 25 - impair 39 16421658242965910275055840472270471049 638728478116949861246791167518480580 1
662 25 - pair 22 1718102501 66775950 1
663 25 - pair 4 103 4 1
664 25 - pair 22 1700902565 66007821 1
665 25 - pair 10 13719 532 1
666 25 - pair 16 27365201 1060380 1
667 25 - pair 14 107119097 4147668 1
668 25 - pair 8 56447 2184 1
669 25 - pair 38 14226117859054135 550013492618436 1
670 25 - pair 14 5791211 223734 1
671 25 - pair 10 58620 2263 1
672 25 - pair 4 337 13 1
673 25 - impair 31 4765506835465395993032041249 183696788896587421699032600 1
674 25 - pair 4 675 26 1
675 25 - pair 2 26 1 1
676 26

n est un carré

677 26 - impair 1 1353 52 1
678 26 - pair 2 677 26 1
679 26 - pair 16 17792625320 682818291 1
680 26 - pair 2 339 13 1
681 26 - pair 24 10743166003415 411679015748 1
682 26 - pair 10 1197901 45870 1
683 26 - pair 14 170067682 6507459 1
684 26 - pair 8 57799 2210 1
685 26 - impair 15 95592800063517769 3652413145693884 1
686 26 - pair 16 10850138895 414260228 1
687 26 - pair 10 165337 6308 1
688 26 - pair 12 24248647 924471 1
689 26 - pair 2 105 4 1
690 26 - pair 6 1471 56 1
691 26 - pair 38 31138100617500578690 1184549173291009383 1
692 26 - pair 14 2499849 95030 1
693 26 - pair 8 246401 9360 1
694 26 - pair 46 38782105445014642382885 1472148590903997672114 1
695 26 - pair 8 33639 1276 1
696 26 - pair 8 1451 55 1
697 26 - impair 3 34849 1320 1
698 26 - impair 9 51999603 1968214 1
699 26 - pair 14 2271050 85899 1
700 26 - pair 16 8193151 309672 1
701 26 - impair 5 277631049 10485980 1
702 26 - pair 2 53 2 1
703 26 - pair 10 1159172 43719 1
704 26 - pair 8 79201 2985 1
705 26 - pair 10 237161 8932 1
706 26 - pair 8 34595 1302 1
707 26 - pair 8 2526 95 1
708 26 - pair 12 62423 2346 1
709 26 - impair 15 665782673992201 25003993164540 1
710 26 - pair 8 1279 48 1
711 26 - pair 4 80 3 1
712 26 - pair 6 1601 60 1
713 26 - pair 14 5286367 197976 1
714 26 - pair 10 4115 154 1
715 26 - pair 10 75646 2829 1
716 26 - pair 28 35115719688199 1312336060110 1
717 26 - pair 12 6998399 261360 1
718 26 - pair 40 8933399183036079503 333391496474140716 1
719 26 - pair 28 403480310400 15047276489 1
720 26 - pair 4 161 6 1
721 26 - pair 40 18632176943292415 693898530122112 1
722 26 - pair 14 22619537 841812 1
723 26 - pair 4 242 9 1
724 26 - pair 42 2469645423824185801 91783649341730970 1
725 26 - pair 6 9801 364 1
726 26 - pair 4 485 18 1
727 26 - pair 4 728 27 1
728 26 - pair 2 27 1 1
729 27

n est un carré

730 27 - impair 1 1459 54 1
731 27 - pair 2 730 27 1
732 27 - pair 2 487 18 1
733 27 - impair 5 195307849 7213860 1
734 27 - pair 12 10394175 383656 1
735 27 - pair 2 244 9 1
736 27 - pair 8 24335 897 1
737 27 - pair 14 252975383 9318468 1
738 27 - pair 2 163 6 1
739 27 - pair 46 98015661073616742153890 3605564376516452758671 1
740 27 - pair 6 9249 340 1
741 27 - pair 10 7352695 270108 1
742 27 - pair 14 263091151 9658380 1
743 27 - pair 8 714024 26195 1
744 27 - pair 10 7501 275 1
745 27 - pair 14 12769001 467820 1
746 27 - impair 13 61268974069299 2243216519470 1
747 27 - pair 2 82 3 1
748 27 - pair 12 5658247 206886 1
749 27 - pair 26 1084616384895 39631020176 1
750 27 - pair 16 2550251 93122 1
751 27 - pair 52 7293318466794882424418960 266136970677206024456793 1
752 27 - pair 8 4607 168 1
753 27 - pair 24 308526027863 11243313484 1
754 27 - impair 9 836977699 30480930 1
755 27 - pair 4 1209 44 1
756 27 - pair 2 55 2 1
757 27 - impair 11 3750107388553 136299971388 1
758 27 - pair 18 413959717 15035694 1
759 27 - pair 6 551 20 1
760 27 - pair 10 52021 1887 1
761 27 - impair 7 1280001 46400 1
762 27 - pair 10 6349 230 1
763 27 - pair 22 719724601 26055780 1
764 27 - pair 32 161784071999999 5853142302000 1
765 27 - pair 10 285769 10332 1
766 27 - pair 44 145933611945744638015 5272795728865625208 1
767 27 - pair 12 31212 1127 1
768 27 - pair 8 18817 679 1
769 27 - impair 37 535781868388881310859702308423201 19320788325040337217824455505160 1
770 27 - pair 4 111 4 1
771 27 - pair 22 2989136930 107651137 1
772 27 - pair 30 6224323426849 224018302020 1
773 27 - impair 11 3607394696649 129748968980 1
774 27 - pair 10 10405 374 1
775 27 - pair 12 4620799 165984 1
776 27 - pair 4 195 7 1
777 27 - pair 4 223 8 1
778 27 - impair 13 5964562960504723 213839942395674 1
779 27 - pair 10 11785490 422259 1
780 27 - pair 4 391 14 1
781 27 - pair 18 67606199 2419140 1
782 27 - pair 4 783 28 1
783 27 - pair 2 28 1 1
784 28

n est un carré

785 28 - impair 1 1569 56 1
786 28 - pair 2 785 28 1
787 28 - pair 18 34625394242 1234262007 1
788 28 - pair 2 393 14 1
789 28 - pair 24 16116667272575 573768548496 1
790 28 - pair 20 6616066879 235389096 1
791 28 - pair 2 225 8 1
792 28 - pair 2 197 7 1
793 28 - pair 4 4393 156 1
794 28 - impair 11 1828310451 64884310 1
795 28 - pair 4 6626 235 1
796 28 - pair 44 529178298454520220799 18756227493635055480 1
797 28 - impair 11 1221759532448649 43276943002540 1
798 28 - pair 2 113 4 1
799 28 - pair 4 424 15 1
800 28 - pair 8 19601 693 1
801 28 - pair 20 500002000001 17666702000 1
802 28 - pair 12 295496099 10434330 1
803 28 - pair 6 7226 255 1
804 28 - pair 10 515095 18166 1
805 28 - pair 18 1514868641 53392104 1
806 28 - pair 14 6166395 217202 1
807 28 - pair 14 51841948 1824923 1
808 28 - pair 18 19731763 694161 1
809 28 - impair 21 376455160998025676163201 13235458622462202510640 1
810 28 - pair 8 27379 962 1
811 28 - pair 38 1382072163578616410 48531117622921197 1
812 28 - pair 2 57 2 1
813 28 - pair 6 2167 76 1
814 28 - pair 28 4206992174549 147454999410 1
815 28 - pair 12 156644 5487 1
816 28 - pair 8 4999 175 1
817 28 - pair 6 343 12 1
818 28 - impair 5 40899 1430 1
819 28 - pair 10 1574 55 1
820 28 - pair 12 39689 1386 1
821 28 - impair 29 9000987377460935993101449 314136625452886403879740 1
822 28 - pair 6 7397 258 1
823 28 - pair 44 235170474903644006168 8197527430497636651 1
824 28 - pair 12 59535 2074 1
825 28 - pair 14 48599 1692 1
826 28 - pair 24 222239304685 7732694382 1
827 28 - pair 10 900602 31317 1
828 28 - pair 6 1151 40 1
829 28 - impair 17 479835713751049 16665383182260 1
830 28 - pair 10 146411 5082 1
831 28 - pair 18 9799705 339948 1
832 28 - pair 12 842401 29205 1
833 28 - pair 14 9478657 328416 1
834 28 - pair 22 6552578705 226897244 1
835 28 - pair 26 34336355806 1188258591 1
836 28 - pair 10 46551 1610 1
837 28 - pair 6 12151 420 1
838 28 - pair 14 42112785797 1454762046 1
839 28 - pair 4 840 29 1
840 28 - pair 2 29 1 1
841 29

n est un carré

842 29 - impair 1 1683 58 1
843 29 - pair 2 842 29 1
844 29 - pair 48 154962314660167628644999 5334022845973817148450 1
845 29 - impair 5 299537289 10304396 1
846 29 - pair 16 2143295 73688 1
847 29 - pair 10 8193151 281520 1
848 29 - pair 6 66249 2275 1
849 29 - pair 30 1501654712948695 51536656330476 1
850 29 - pair 4 2449 84 1
851 29 - pair 12 8418574 288585 1
852 29 - pair 8 194399 6660 1
853 29 - impair 23 215454135724113414336120649 7377009103065498851032020 1
854 29 - pair 8 1294299 44290 1
855 29 - pair 4 3041 104 1
856 29 - pair 26 695359189925 23766887823 1
857 29 - impair 17 131822292741249 4502963741200 1
858 29 - pair 4 703 24 1
859 29 - pair 46 2058844771979643060124010 70246877103894937291269 1
860 29 - pair 4 3871 132 1
861 29 - pair 16 541601801 18457740 1
862 29 - pair 40 358022566147312125503 12194296994921665128 1
863 29 - pair 20 18524026608 630565199 1
864 29 - pair 12 470449 16005 1
865 29 - impair 19 242688628535063329 8251660923733224 1
866 29 - pair 8 42435 1442 1
867 29 - pair 6 70226 2385 1
868 29 - pair 8 3844063 130476 1
869 29 - pair 28 60192738698751 2041898807200 1
870 29 - pair 2 59 2 1
871 29 - pair 24 19442812076 658794555 1
872 29 - pair 10 126003 4267 1
873 29 - pair 18 62809633 2125784 1
874 29 - pair 8 3725 126 1
875 29 - pair 16 120126 4061 1
876 29 - pair 8 10951 370 1
877 29 - impair 15 116476476553 3933131148 1
878 29 - pair 16 9314703 314356 1
879 29 - pair 18 107245324 3617295 1
880 29 - pair 4 89 3 1
881 29 - impair 25 22606256615916825861249 761624136944072910800 1
882 29 - pair 8 19601 660 1
883 29 - pair 46 34878475759617272473442 1173754162936357802169 1
884 29 - pair 8 1665 56 1
885 29 - pair 4 119 4 1
886 29 - pair 54 7743524593057655851637765 260148796464024194850378 1
887 29 - pair 12 469224 15755 1
888 29 - pair 4 149 5 1
889 29 - pair 42 13231974717803657215 443786188413453504 1
890 29 - pair 4 179 6 1
891 29 - pair 8 3970 133 1
892 29 - pair 8 100351 3360 1
893 29 - pair 22 6091434999 203842100 1
894 29 - pair 4 299 10 1
895 29 - pair 4 359 12 1
896 29 - pair 4 449 15 1
897 29 - pair 4 599 20 1
898 29 - pair 4 899 30 1
899 29 - pair 2 30 1 1
900 30

n est un carré

901 30 - impair 1 1801 60 1
902 30 - pair 2 901 30 1
903 30 - pair 2 601 20 1
904 30 - pair 2 451 15 1
905 30 - pair 2 361 12 1
906 30 - pair 2 301 10 1
907 30 - pair 42 123823410343073497682 4111488857741309517 1
908 30 - pair 8 102151 3390 1
909 30 - pair 8 80801 2680 1
910 30 - pair 2 181 6 1
911 30 - pair 24 371832584927520 12319363142953 1
912 30 - pair 2 151 5 1
913 30 - pair 32 515734243080407 17068312251564 1
914 30 - impair 5 62563299 2069410 1
915 30 - pair 2 121 4 1
916 30 - pair 14 5848201 193230 1
917 30 - pair 16 823604599 27197820 1
918 30 - pair 10 4120901 136010 1
919 30 - pair 60 4481603010937119451551263720 147834442396536759781499589 1
920 30 - pair 2 91 3 1
921 30 - pair 34 2522057712835735 83104627139412 1
922 30 - impair 19 351605368773852499 11579506138834350 1
923 30 - pair 6 638 21 1
924 30 - pair 8 11551 380 1
925 30 - impair 5 1555849 51156 1
926 30 - pair 28 304560297142335 10008472361032 1
927 30 - pair 8 227528 7473 1
928 30 - pair 16 768555217 25229061 1
929 30 - impair 19 13224937103288377430049 433896111669844912840 1
930 30 - pair 2 61 2 1
931 30 - pair 22 6681448801 218975640 1
932 30 - pair 22 1072400673 35127652 1
933 30 - pair 8 75263 2464 1
934 30 - pair 14 3034565 99294 1
935 30 - pair 8 1376 45 1
936 30 - pair 8 5201 170 1
937 30 - impair 33 480644425002415999597113107233 15701968936415353889062192632 1
938 30 - pair 10 17151 560 1
939 30 - pair 10 122695 4004 1
940 30 - pair 8 4231 138 1
941 30 - impair 17 1068924905989944201 34845956052079180 1
942 30 - pair 8 106133 3458 1
943 30 - pair 6 737 24 1
944 30 - pair 16 561799 18285 1
945 30 - pair 10 275561 8964 1
946 30 - pair 30 45225786400145 1470417148788 1
947 30 - pair 22 13509645362 439004487 1
948 30 - pair 10 228151 7410 1
949 30 - impair 27 609622436806639069525576201 19789181711517243032971740 1
950 30 - pair 16 202501 6570 1
951 30 - pair 18 224208076 7270445 1
952 30 - pair 8 11663 378 1
953 30 - impair 21 15090531843660371073 488830275367615376 1
954 30 - pair 14 32080051 1038630 1
955 30 - pair 16 2095256249 67800900 1
956 30 - pair 32 76759023628799 2482564242480 1
957 30 - pair 6 14849 480 1
958 30 - pair 36 16762522330425599 541572514048560 1
959 30 - pair 4 960 31 1
960 30 - pair 2 31 1 1
961 31

n est un carré

962 31 - impair 1 1923 62 1
963 31 - pair 2 962 31 1
964 31 - pair 34 10085143557001249 324820602522300 1
965 31 - impair 5 446526729 14374204 1
966 31 - pair 6 57499 1850 1
967 31 - pair 32 4649532557817485528 149518887194649693 1
968 31 - pair 6 19601 630 1
969 31 - pair 16 13588951 436540 1
970 31 - impair 9 215395035859 6915917802 1
971 31 - pair 22 12479806786330 400496058813 1
972 31 - pair 20 9863382151 316368130 1
973 31 - pair 8 903223 28956 1
974 31 - pair 32 488825745235215 15662987185124 1
975 31 - pair 4 1249 40 1
976 31 - pair 18 1766319049 56538495 1
977 31 - impair 19 108832847723078562849 3481871275306470280 1
978 31 - pair 10 118337 3784 1
979 31 - pair 10 360449 11520 1
980 31 - pair 10 51841 1656 1
981 31 - pair 30 158070671986249 5046808151700 1
982 31 - pair 6 8837 282 1
983 31 - pair 8 284088 9061 1
984 31 - pair 10 88805 2831 1
985 31 - impair 5 332929 10608 1
986 31 - impair 3 49299 1570 1
987 31 - pair 4 377 12 1
988 31 - pair 16 14549450527 462879684 1
989 31 - pair 32 550271588560695 17497618534396 1
990 31 - pair 4 881 28 1
991 31 - pair 60 379516400906811930638014896080 12055735790331359447442538767 1
992 31 - pair 2 63 2 1
993 31 - pair 6 2647 84 1
994 31 - pair 6 1135 36 1
995 31 - pair 12 8835999 280120 1
996 31 - pair 20 8553815 271038 1
997 31 - impair 13 14418057673 456624468 1
998 31 - pair 18 984076901 31150410 1
999 31 - pair 18 102688615 3248924 1
1000 31 - pair 18 39480499 1248483 1