不定方程a^2=a*b^2-b^2*c+a^2*c的整数解

yangchuanju · 发表于 2024-7-7 07:04

对于命题（一），c=1,19,37,73,91,109,127,163,181,199,217,253,271,289，……
19 is prime
37 is prime
73 is prime
91=7*13
109 is prime
127 is prime
163 is prime
181 is prime
199 is prime
217=7*31
253=11*23
271 is prime
289=17*17
307 is prime
343=7*7*7
361=19*19
379 is prime
397 is prime
433 is prime
451=11*41
469=7*67
487 is prime
523 is prime
541 is prime
559=13*43
577 is prime
613 is prime
631 is prime
649=11*59
667=23*29
703=19*37
721=7*103
739 is prime
757 is prime
793=13*61
811 is prime
829 is prime
847=7*11*11
883 is prime
901=17*53
919 is prime
937 is prime
973=7*139
991 is prime
1009 is prime
1027=13*79
1063 is prime
1081=23*47
1099=7*157
1117 is prime
1153 is prime
1171 is prime
1189=29*41
1207=17*71
1243=11*113
1261=13*97
1279 is prime
1297 is prime
1333=31*43
1351=7*193
1369=37*37
1387=19*73
1423 is prime
1441=11*131
1459 is prime
1477=7*211
1513=17*89
1531 is prime
1549 is prime
1567 is prime
1603=7*229
1621 is prime
1639=11*149
1657 is prime
1693 is prime
1711=29*59
1729=7*13*19
1747 is prime
1783 is prime
1801 is prime
1819=17*107
1837=11*167
1873 is prime
1891=31*61
1909=23*83
1927=41*47
1963=13*151
1981=7*283
1999 is prime
2017 is prime
2053 is prime
2071=19*109
2089 is prime
2107=7*7*43
2143 is prime
2161 is prime
2179 is prime
2197=13*13*13
2233=7*11*29
2251 is prime
2269 is prime
2287 is prime
2323=23*101
2341 is prime
2359=7*337
2377 is prime
2413=19*127
2431=11*13*17
2449=31*79
2467 is prime
2503 is prime
2521 is prime
2539 is prime
2557 is prime
2593 is prime
2611=7*373
2629=11*239
2647 is prime
2683 is prime
2701=37*73
2719 is prime
2737=7*17*23
2773=47*59
2791 is prime
2809=53*53
2827=11*257
2863=7*409
2881=43*67
2899=13*223
2917 is prime
2953 is prime
2971 is prime
2989=7*7*61
3007=31*97
3043=17*179
3061 is prime
3079 is prime
3097=19*163
3133=13*241
3151=23*137
3169 is prime
3187 is prime
3223=11*293
3241=7*463
3259 is prime
3277=29*113
3313 is prime
3331 is prime
3349=17*197
3367=7*13*37
3403=41*83
3421=11*311
3439=19*181
3457 is prime
3493=7*499
3511 is prime
3529 is prime
3547 is prime
3583 is prime
3601=13*277
3619=7*11*47
3637 is prime
3673 is prime
3691 is prime
3709 is prime
3727 is prime
3763=53*71
3781=19*199
3799=29*131
3817=11*347
3853 is prime
3871=7*7*79
3889 is prime
3907 is prime
3943 is prime
3961=17*233
3979=23*173
3997=7*571
4033=37*109
4051 is prime
4069=13*313
4087=61*67
4123=7*19*31
4141=41*101
4159 is prime
4177 is prime
4213=11*383
4231 is prime
4249=7*607
4267=17*251
4303=13*331
4321=29*149
4339 is prime
4357 is prime
4393=23*191
4411=11*401
4429=43*103
4447 is prime
4483 is prime
4501=7*643
4519 is prime
4537=13*349
4573=17*269
4591 is prime
4609=11*419
4627=7*661
4663 is prime
4681=31*151
4699=37*127
4717=53*89
4753=7*7*97
4771=13*367
4789 is prime
4807=11*19*23
4843=29*167
4861 is prime
4879=7*17*41
4897=59*83
4933 is prime
4951 is prime
4969 is prime
4987 is prime
5023 is prime
5041=71*71
5059 is prime
5077 is prime
5113 is prime
5131=7*733
5149=19*271
5167 is prime
5203=11*11*43
5221=23*227
5239=13*13*31
5257=7*751
5293=67*79
5311=47*113
5329=73*73
5347 is prime
5383=7*769
5401=11*491
5419 is prime
5437 is prime
5473=13*421
5491=17*17*19
5509=7*787
5527 is prime
5563 is prime
5581 is prime
5599=11*509
5617=41*137
5653 is prime
5671=53*107
5689 is prime
5707=13*439
5743 is prime
5761=7*823
5779 is prime
5797=11*17*31
5833=19*307
5851 is prime
5869 is prime
5887=7*29*29
5923 is prime
5941=13*457
5959=59*101
5977=43*139
6013=7*859
6031=37*163
6049=23*263
6067 is prime
6103=17*359
6121 is prime
6139=7*877
6157=47*131
6193=11*563
6211 is prime
6229 is prime
6247 is prime
6283=61*103
6301 is prime
6319=71*89
6337 is prime
6373 is prime
6391=7*11*83
6409=13*17*29
6427 is prime
6463=23*281
6481 is prime
6499=67*97
6517=7*7*7*19
6553 is prime
6571 is prime
6589=11*599
6607 is prime
6643=7*13*73
6661 is prime
6679 is prime
6697=37*181
6733 is prime
6751=43*157
6769=7*967
6787=11*617
6823 is prime
6841 is prime
6859=19*19*19
6877=13*23*23
6913=31*223
6931=29*239
6949 is prime
6967 is prime
7003=47*149
7021=7*17*59
7039 is prime
7057 is prime
7093=41*173
7111=13*547
7129 is prime
7147=7*1021
7183=11*653
7201=19*379
7219 is prime
7237 is prime
7273=7*1039
7291=23*317
7309 is prime
7327=17*431
7363=37*199
7381=11*11*61
7399=7*7*151
7417 is prime
7453=29*257
7471=31*241
7489 is prime
7507 is prime
7543=19*397
7561 is prime
7579=11*13*53
7597=71*107
7633=17*449
7651=7*1093
7669 is prime
7687 is prime
7723 is prime
7741 is prime
7759 is prime
7777=7*11*101
7813=13*601
7831=41*191
7849=47*167
7867 is prime
7903=7*1129
7921=89*89
7939=17*467
7957=73*109
7993 is prime
8011 is prime
8029=7*31*37
8047=13*619
8083=59*137
8101 is prime
8119=23*353
8137=79*103
8173=11*743
8191 is prime
8209 is prime
8227=19*433
8263 is prime
8281=7*7*13*13
8299=43*193
8317 is prime
8353 is prime
8371=11*761
8389 is prime
8407=7*1201
8443 is prime
8461 is prime
8479=61*139
8497=29*293
8533=7*23*53
8551=17*503
8569=11*19*41
8587=31*277
8623 is prime
8641 is prime
8659=7*1237
8677 is prime
8713 is prime
8731 is prime
8749=13*673
8767=11*797
8803 is prime
8821 is prime
8839 is prime
8857=17*521
8893 is prime
8911=7*19*67
8929 is prime
8947=23*389
8983=13*691
9001 is prime
9019=29*311
9037=7*1291
9073=43*211
9091 is prime
9109 is prime
9127 is prime
9163=7*7*11*17
9181 is prime
9199 is prime
9217=13*709
9253=19*487
9271=73*127
9289=7*1327
9307=41*227
9343 is prime
9361=11*23*37
9379=83*113
9397 is prime
9433 is prime
9451=13*727
9469=17*557
9487=53*179
9523=89*107
9541=7*29*47
9559=11*11*79
9577=61*157
9613 is prime
9631 is prime
9649 is prime
9667=7*1381
9703=31*313
9721 is prime
9739 is prime
9757=11*887
9793=7*1399
9811 is prime
9829 is prime
9847=43*229
9883 is prime
9901 is prime
9919=7*13*109
9937=19*523
9973 is prime
9991=97*103

yangchuanju · 发表于 2024-7-7 07:07

其中的三合数、四合数有：
343 7 7 7
847 7 11 11
1729 7 13 19
2107 7 7 43
2197 13 13 13
2233 7 11 29
2431 11 13 17
2737 7 17 23
2989 7 7 61
3367 7 13 37
3619 7 11 47
3871 7 7 79
4123 7 19 31
4753 7 7 97
4807 11 19 23
4879 7 17 41
5203 11 11 43
5239 13 13 31
5491 17 17 19
5797 11 17 31
5887 7 29 29
6391 7 11 83
6409 13 17 29
6643 7 13 73
6859 19 19 19
6877 13 23 23
7021 7 17 59
7381 11 11 61
7399 7 7 151
7579 11 13 53
7777 7 11 101
8029 7 31 37
8533 7 23 53
8569 11 19 41
8911 7 19 67
9361 11 23 37
9541 7 29 47
9559 11 11 79
9919 7 13 109
8281 7 7 13 13
6517 7 7 7 19
9163 7 7 11 17
它们的整数解都是太阳命题（一）的反例！

yangchuanju · 发表于 2024-7-7 07:11

命题（三）可取c数
49=7*7
77=7*11
119=7*17
121=11*11
133=7*19
143=11*13
161=7*23
169=13*13
187=11*17
203=7*29
209=11*19
221=13*17
247=13*19
259=7*37
287=7*41
299=13*23
301=7*43
319=11*29
323=17*19
329=7*47
341=11*31
371=7*53
377=13*29
391=17*23
403=13*31
407=11*37
413=7*59
427=7*61
437=19*23
473=11*43
481=13*37
493=17*29
497=7*71
511=7*73
517=11*47
527=17*31
529=23*23
533=13*41
539=7*7*11
551=19*29
553=7*79
581=7*83
583=11*53
589=19*31
611=13*47
623=7*89
629=17*37
637=7*7*13
671=11*61
679=7*97
689=13*53
697=17*41
707=7*101
713=23*31
731=17*43
737=11*67
749=7*107
763=7*109
767=13*59
779=19*41
781=11*71
791=7*113
799=17*47
803=11*73
817=19*43
833=7*7*17
841=29*29
851=23*37
869=11*79
871=13*67
889=7*127
893=19*47
899=29*31
913=11*83
917=7*131
923=13*71
931=7*7*19
943=23*41
949=13*73
959=7*137
961=31*31
979=11*89
989=23*43
1001=7*11*13
1003=17*59
1007=19*53
1037=17*61
1043=7*149
1057=7*151
1067=11*97
1073=29*37
1079=13*83
1111=11*101
1121=19*59
1127=7*7*23
1133=11*103
1139=17*67
1141=7*163
1147=31*37
1157=13*89
1159=19*61
1169=7*167
1177=11*107
1183=7*13*13
1199=11*109
1211=7*173
1219=23*53
1241=17*73
1247=29*43
1253=7*179
1267=7*181
1271=31*41
1273=19*67
1309=7*11*17
1313=13*101
1331=11*11*11
1337=7*191
1339=13*103
1343=17*79
1349=19*71
1357=23*59
1363=29*47
1379=7*197
1391=13*107
1393=7*199
1397=11*127
1403=23*61
1411=17*83
1417=13*109
1421=7*7*29
1457=31*47
1463=7*11*19
1469=13*113
1501=19*79
1507=11*137
1517=37*41
1519=7*7*31
1529=11*139
1537=29*53
1541=23*67
1547=7*13*17
1561=7*223
1573=11*11*13
1577=19*83
1589=7*227
1591=37*43
1631=7*233
1633=23*71
1643=31*53
1649=17*97
1651=13*127
1661=11*151
1673=7*239
1679=23*73
1681=41*41
1687=7*241
1691=19*89
1703=13*131
1717=17*101
1727=11*157
1739=37*47
1751=17*103
1757=7*251
1763=41*43
1769=29*61
1771=7*11*23
1781=13*137
1793=11*163
1799=7*257
1807=13*139
1813=7*7*37
1817=23*79
1829=31*59
1841=7*263
1843=19*97
1849=43*43
1853=17*109
1859=11*13*13
1883=7*269
1897=7*271
1903=11*173
1919=19*101
1921=17*113
1937=13*149
1939=7*277
1943=29*67
1957=19*103
1961=37*53
1967=7*281
1969=11*179
1991=11*181
……

yangchuanju · 发表于 2024-7-7 07:14

其中的三合数、四合数有：
c p1 p2 p3 p4
2401 7 7 7 7
3773 7 7 7 11
4459 7 7 7 13
5831 7 7 7 17
5929 7 7 11 11
7007 7 7 11 13
7889 7 7 7 23
9317 7 11 11 11
9947 7 7 7 29
539 7 7 11
637 7 7 13
833 7 7 17
931 7 7 19
1001 7 11 13
1127 7 7 23
1183 7 13 13
1309 7 11 17
1331 11 11 11
1421 7 7 29
1463 7 11 19
1519 7 7 31
1547 7 13 17
1573 11 11 13
1771 7 11 23
1813 7 7 37
1859 11 13 13
2009 7 7 41
2023 7 17 17
2057 11 11 17
2093 7 13 23
2261 7 17 19
2299 11 11 19
2303 7 7 47
2387 7 11 31
2527 7 19 19
2597 7 7 53
2639 7 13 29
2717 11 13 19
2783 11 11 23
2821 7 13 31
2849 7 11 37
2873 13 13 17
2891 7 7 59
3059 7 19 23
3157 7 11 41
3179 11 17 17
3211 13 13 19
3283 7 7 67
3289 11 13 23
3311 7 11 43
3451 7 17 29
3479 7 7 71
3509 11 11 29
3553 11 17 19
3577 7 7 73
3689 7 17 31
3703 7 23 23
3731 7 13 41
3751 11 11 31
3757 13 17 17
3857 7 19 29
3887 13 13 23
3913 7 13 43
3971 11 19 19
4067 7 7 83
4081 7 11 53
4147 11 13 29
4199 13 17 19
4277 7 13 47
4301 11 17 23
4361 7 7 89
4403 7 17 37
4433 11 13 31
4477 11 11 37
4543 7 11 59
4669 7 23 29
4693 13 19 19
4697 7 11 61
4823 7 13 53
4901 13 13 29
4913 17 17 17
4921 7 19 37
4949 7 7 101
4961 11 11 41
4991 7 23 31
5047 7 7 103
5083 13 17 23
5117 7 17 43
5159 7 11 67
5243 7 7 107
5291 11 13 37
5341 7 7 109
5369 7 13 59
5423 11 17 29
5453 7 19 41
5467 7 11 71
5537 7 7 113
5551 7 13 61
5593 7 17 47
5621 7 11 73
5681 13 19 23
5687 11 11 47
5719 7 19 43
5819 11 23 23
5863 11 13 41
5957 7 23 37
6061 11 19 29
6083 7 11 79
6097 7 13 67
6137 17 19 19
6149 11 13 43
6223 7 7 127
6251 7 19 47
6253 13 13 37
6293 7 29 31
6307 7 17 53
6413 11 11 53
6419 7 7 131
6461 7 13 71
6479 11 19 31
6601 7 23 41
6647 17 17 23
6713 7 7 137
6721 11 13 47
6727 7 31 31
6811 7 7 139
6851 13 17 31
6853 7 11 89
6919 11 17 37
6923 7 23 43
6929 13 13 41
7049 7 19 53
7139 11 11 59
7163 13 19 29
7189 7 13 79
7259 7 17 61
7267 13 13 43
7301 7 7 149
7337 11 23 29
7429 17 19 23
7469 7 11 97
7511 7 29 37
7553 7 13 83
7567 7 23 47
7657 13 19 31
7667 11 17 41
7693 7 7 157
7733 11 19 37
7843 11 23 31
7847 7 19 59
7931 7 11 103
7943 13 13 47
7973 7 17 67
7987 7 7 163
8041 11 17 43
8099 7 13 89
8107 11 11 67
8113 7 19 61
8177 13 17 37
8183 7 7 167
8239 7 11 107
8303 19 19 23
8323 7 29 41
8381 17 17 29
8393 7 11 109
8437 11 13 59
8449 7 17 71
8477 7 7 173
8591 11 11 71
8671 13 23 29
8687 7 17 73
8701 7 11 113
8723 11 13 61
8729 7 29 43
8771 7 7 179
8789 11 17 47
8827 7 13 97
8833 11 11 73
8869 7 7 181
8897 7 31 41
8957 13 13 53
8959 17 17 31
8987 11 19 43
8993 17 23 23
9061 13 17 41
9139 13 19 37
9191 7 13 101
9251 11 29 29
9269 13 23 31
9331 7 31 43
9359 7 7 191
9367 17 19 29
9373 7 13 103
9401 7 17 79
9443 7 19 71
9457 7 7 193
9499 7 23 59
9503 13 17 43
9581 11 13 67
9583 7 37 37
9653 7 7 197
9709 7 19 73
9737 7 13 107
9751 7 7 199
9779 7 11 127
9821 7 23 61
9823 11 19 47
9877 7 17 83
9889 11 29 31
9911 11 17 53
9971 13 13 59
当c取这些三合数、四合数时的整数解都是太阳命题3的反例！

yangchuanju · 发表于 2024-7-7 17:20

yangchuanju 发表于 2024-7-7 06:33
笔者，详细研究了不定方程a^2=a*b^2-b^2*c+a^2*c的整数解构成和分布，
当c取（一）中的奇数（包括5的倍数 ...

对于c=163,487,811……各有第2组整数解

等差数列c=163,487,811时的整数解预测：
c 解数 a1 b1 a2 b2
163 2 145 435 161 1449
487 2 433 1299 481 4329
811 2 721 2163 801 7209
1135 2 1009 3027 1121 10089
1459 2 1297 3891 1441 12969
1783 2 1585 4755 1761 15849
2107 2 1873 5619 2081 18729
2431 2 2161 6483 2401 21609
2755 2 2449 7347 2721 24489
3079 2 2737 8211 3041 27369
3403 2 3025 9075 3361 30249
……
b1/a1=3，b2/a2=9， a1增288，a2增320，a2-a1分别等于16,48,80,112,144……；
经逐个检验，预测正确！

yangchuanju · 发表于 2024-7-7 17:25

本帖最后由 yangchuanju 于 2024-7-7 17:33 编辑

等差数列c=883,2647,4411……时的整数解预测（各2组，b/a=3,7)及检验：
a b c a^2 a*b^2-b^2*c+a^2*c 检验 b/a
785 2355 883 616225 616225 0 3
2353 7059 2647 5536609 5536609 0 3
3921 11763 4411 15374241 15374241 0 3
5489 16467 6175 30129121 30129121 0 3
7057 21171 7939 49801249 49801249 0 3
865 6055 883 748225 748225 0 7
2593 18151 2647 6723649 6723649 0 7
4321 30247 4411 18671041 18671041 0 7
6049 42343 6175 36590401 36590401 0 7
7777 54439 7939 60481729 60481729 0 7
检验正确！

yangchuanju · 发表于 2024-7-7 17:34

等差数列c=451,1351,2251……时的整数解预测（至少3组，b/a=3,5,15)及检验：
a b c a^2 a*b^2-b^2*c+a^2*c 检验 b/a
401 1203 451 160801 160801 0 3
1201 3603 1351 1442401 1442401 0 3
2001 6003 2251 4004001 4004001 0 3
2801 8403 3151 7845601 7845601 0 3
3601 10803 4051 12967201 12967201 0 3
4401 13203 4951 19368801 19368801 0 3
5201 15603 5851 27050401 27050401 0 3
6001 18003 6751 36012001 36012001 0 3
6801 20403 7651 46253601 46253601 0 3
7601 22803 8551 57775201 57775201 0 3
8401 25203 9451 70576801 70576801 0 3
9201 27603 10351 84658401 84658401 0 3
433 2165 451 187489 187489 0 5
1297 6485 1351 1682209 1682209 0 5
2161 10805 2251 4669921 4669921 0 5
3025 15125 3151 9150625 9150625 0 5
3889 19445 4051 15124321 15124321 0 5
4753 23765 4951 22591009 22591009 0 5
5617 28085 5851 31550689 31550689 0 5
6481 32405 6751 42003361 42003361 0 5
7345 36725 7651 53949025 53949025 0 5
8209 41045 8551 67387681 67387681 0 5
9073 45365 9451 82319329 82319329 0 5
9937 49685 10351 98743969 98743969 0 5
10801 54005 11251 116661601 116661601 0 5
449 6735 451 201601 201601 0 15
1345 20175 1351 1809025 1809025 0 15
2241 33615 2251 5022081 5022081 0 15
3137 47055 3151 9840769 9840769 0 15
4033 60495 4051 16265089 16265089 0 15
4929 73935 4951 24295041 24295041 0 15
5825 87375 5851 33930625 33930625 0 15
6721 100815 6751 45171841 45171841 0 15
7617 114255 7651 58018689 58018689 0 15
8513 127695 8551 72471169 72471169 0 15
9409 141135 9451 88529281 88529281 0 15
10305 154575 10351 106193025 106193025 0 15
209 285 451 43681 43681 0 1.363636364
1057 2265 1351 1117249 1117249 0 2.142857143
经逐个检验，预测正确！

yangchuanju · 发表于 2024-7-7 17:40

c=7939（163类+883类),4051（163类+451类)的整数解预测及检验：
a b c a^2 a*b^2-b^2*c+a^2*c 检验 b/a
7057 21171 7939 49801249 49801249 0 3
7777 54439 7939 60481729 60481729 0 7
7841 70569 7939 61481281 61481281 0 9

3601 10803 4051 12967201 12967201 0 3
3889 19445 4051 15124321 15124321 0 5
4001 36009 4051 16008001 16008001 0 9
4033 60495 4051 16265089 16265089 0 15

yangchuanju · 发表于 2024-7-7 17:48

下列各个c，至少有一组b/a=3的整数解：
c a b b/a a增
19 17 51 3 ——
55 49 147 3 32
91 81 243 3 32
127 113 339 3 32
163 145 435 3 32
199 177 531 3 32
235 209 627 3 32
271 241 723 3 32
307 273 819 3 32
343 305 915 3 32
379 337 1011 3 32
415 369 1107 3 32
451 401 1203 3 32
487 433 1299 3 32
523 465 1395 3 32
559 497 1491 3 32
595 529 1587 3 32
631 561 1683 3 32
667 593 1779 3 32
703 625 1875 3 32
739 657 1971 3 32
775 689 2067 3 32
811 721 2163 3 32
847 753 2259 3 32
883 785 2355 3 32
919 817 2451 3 32
955 849 2547 3 32
991 881 2643 3 32
1027 913 2739 3 32
1063 945 2835 3 32
1099 977 2931 3 32
1135 1009 3027 3 32
1171 1041 3123 3 32
1207 1073 3219 3 32
1243 1105 3315 3 32
1279 1137 3411 3 32
1315 1169 3507 3 32
1351 1201 3603 3 32
1387 1233 3699 3 32
1423 1265 3795 3 32
1459 1297 3891 3 32
1495 1329 3987 3 32
1531 1361 4083 3 32
1567 1393 4179 3 32
1603 1425 4275 3 32
1639 1457 4371 3 32
1675 1489 4467 3 32
1711 1521 4563 3 32
1747 1553 4659 3 32
1783 1585 4755 3 32
1819 1617 4851 3 32
1855 1649 4947 3 32
1891 1681 5043 3 32
1927 1713 5139 3 32
1963 1745 5235 3 32
1999 1777 5331 3 32
2035 1809 5427 3 32
2071 1841 5523 3 32
2107 1873 5619 3 32
2143 1905 5715 3 32
2179 1937 5811 3 32
2215 1969 5907 3 32
2251 2001 6003 3 32
2287 2033 6099 3 32
2323 2065 6195 3 32
2359 2097 6291 3 32
2395 2129 6387 3 32
2431 2161 6483 3 32
2467 2193 6579 3 32
2503 2225 6675 3 32
2539 2257 6771 3 32
2575 2289 6867 3 32
2611 2321 6963 3 32
2647 2353 7059 3 32
2683 2385 7155 3 32
2719 2417 7251 3 32
2755 2449 7347 3 32
2791 2481 7443 3 32
2827 2513 7539 3 32
2863 2545 7635 3 32
2899 2577 7731 3 32
2935 2609 7827 3 32
2971 2641 7923 3 32
3007 2673 8019 3 32

yangchuanju · 发表于 2024-7-7 17:57

163系列参数c，两个整数解的b/a=3和9：
163 9235 18307
487 9559 18631
811 9883 18955
1135 10207 19279
1459 10531 19603
1783 10855 19927
2107 11179 20251
2431 11503 20575
2755 11827 20899
3079 12151 21223
3403 12475 21547
3727 12799 21871
4051 13123 22195
4375 13447 22519
4699 13771 22843
5023 14095 23167
5347 14419 23491
5671 14743 23815
5995 15067 24139
6319 15391 24463
6643 15715 24787
6967 16039 25111
7291 16363 25435
7615 16687 25759
7939 17011 26083
8263 17335 26407
8587 17659 26731
8911 17983 27055

883系列参数c，两个整数解的b/a=3和7：
883
2647
4411
6175
7939
9703
11467
13231
14995
16759
18523
20287
22051

451系列参数c，三个整数解的b/a=3,5和15：
451
1351
2251
3151
4051
4951
5851
6751
7651
8551
9451
10351
11251
12151
13051
13951
14851
15751
16651
17551
18451
19351
20251

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