The triplets (M, b, c) for M=(2n+1) up to n=50000 are: (3, 23, 204), (5, 118, 2940), (7, 333, 16296), (9, 716, 57960), (11, 1315, 159060), (13, 2178, 368004), (15, 3353, 754320), (17, 4888, 1412496), (19, 6831, 2465820), (21, 9230, 4070220), (23, 12133, 6418104), (25, 15588, 9742200), (27, 19643, 14319396), (29, 24346, 20474580), (31, 29745, 28584480), (33, 35888, 39081504), (35, 42823, 52457580), (37, 50598, 69267996), (39, 59261, 90135240), (41, 68860, 115752840), (43, 79443, 146889204), (45, 91058, 184391460), (47, 103753, 229189296), (49, 117576, 282298800), (51, 132575, 344826300), (53, 148798, 417972204), (55, 166293, 503034840), (57, 185108, 601414296), (59, 205291, 714616260), (61, 226890, 844255860), (63, 249953, 992061504), (65, 274528, 1159878720), (67, 300663, 1349673996), (69, 328406, 1563538620), (71, 357805, 1803692520), (73, 388908, 2072488104), (75, 421763, 2372414100), (77, 456418, 2706099396), (79, 492921, 3076316880), (81, 531320, 3485987280), (83, 571663, 3938183004), (85, 613998, 4436131980), (87, 658373, 4983221496), (89, 704836, 5583002040), (91, 753435, 6239191140), (93, 804218, 6955677204), (95, 857233, 7736523360), (97, 912528, 8585971296), (99, 970151, 9508445100), (101, 1030150, 10508555100), (103, 1092573, 11591101704), (105, 1157468, 12761079240), (107, 1224883, 14023679796), (109, 1294866, 15384297060), (111, 1367465, 16848530160), (113, 1442728, 18422187504), (115, 1520703, 20111290620), (117, 1601438, 21922077996), (119, 1684981, 23861008920), (121, 1771380, 25934767320), (123, 1860683, 28150265604), (125, 1952938, 30514648500), (127, 2048193, 33035296896), (129, 2146496, 35719831680), (131, 2247895, 38576117580), (133, 2352438, 41612267004), (135, 2460173, 44836643880), (137, 2571148, 48257867496), (139, 2685411, 51884816340), (141, 2803010, 55726631940), (143, 2923993, 59792722704), (145, 3048408, 64092767760), (147, 3176303, 68636720796), (149, 3307726, 73434813900), (151, 3442725, 78497561400), (153, 3581348, 83835763704), (155, 3723643, 89460511140), (157, 3869658, 95383187796), (159, 4019441, 101615475360), (161, 4173040, 108169356960), (163, 4330503, 115057121004), (165, 4491878, 122291365020), (167, 4657213, 129884999496), (169, 4826556, 137851251720), (171, 4999955, 146203669620), (173, 5177458, 154956125604), (175, 5359113, 164122820400), (177, 5544968, 173718286896), (179, 5735071, 183757393980), (181, 5929470, 194255350380), (183, 6128213, 205227708504), (185, 6331348, 216690368280), (187, 6538923, 228659580996), (189, 6750986, 241151953140), (191, 6967585, 254184450240), (193, 7188768, 267774400704), (195, 7414583, 281939499660), (197, 7645078, 296697812796), (199, 7880301, 312067780200), (201, 8120300, 328068220200), (203, 8365123, 344718333204), (205, 8614818, 362037705540), (207, 8869433, 380046313296), (209, 9129016, 398764526160), (211, 9393615, 418213111260), (213, 9663278, 438413237004), (215, 9938053, 459386476920), (217, 10217988, 481154813496), (219, 10503131, 503740642020), (221, 10793530, 527166774420), (223, 11089233, 551456443104), (225, 11390288, 576633304800), (227, 11696743, 602721444396), (229, 12008646, 629745378780), (231, 12326045, 657730060680), (233, 12648988, 686700882504), (235, 12977523, 716683680180), (237, 13311698, 747704736996), (239, 13651561, 779790787440), (241, 13997160, 812969021040), (243, 14348543, 847267086204), (245, 14705758, 882713094060), (247, 15068853, 919335622296), (249, 15437876, 957163719000), (251, 15812875, 996226906500), (253, 16193898, 1036555185204), (255, 16580993, 1078179037440), (257, 16974208, 1121129431296), (259, 17373591, 1165437824460), (261, 17779190, 1211136168060), (263, 18191053, 1258256910504), (265, 18609228, 1306833001320), (267, 19033763, 1356897894996), (269, 19464706, 1408485554820), (271, 19902105, 1461630456720), (273, 20346008, 1516367593104), (275, 20796463, 1572732476700), (277, 21253518, 1630761144396), (279, 21717221, 1690490161080), (281, 22187620, 1751956623480), (283, 22664763, 1815198164004), (285, 23148698, 1880252954580), (287, 23639473, 1947159710496), (289, 24137136, 2015957694240), (291, 24641735, 2086686719340), (293, 25153318, 2159387154204), (295, 25671933, 2234099925960), (297, 26197628, 2310866524296), (299, 26730451, 2389729005300), (301, 27270450, 2470729995300), (303, 27817673, 2553912694704), (305, 28372168, 2639320881840), (307, 28933983, 2726998916796), (309, 29503166, 2816991745260), (311, 30079765, 2909344902360), (313, 30663828, 3004104516504), (315, 31255403, 3101317313220), (317, 31854538, 3201030618996), (319, 32461281, 3303292365120), (321, 33075680, 3408151091520), (323, 33697783, 3515655950604), (325, 34327638, 3625856711100), (327, 34965293, 3738803761896), (329, 35610796, 3854548115880), (331, 36264195, 3973141413780), (333, 36925538, 4094635928004), (335, 37594873, 4219084566480), (337, 38272248, 4346540876496), (339, 38957711, 4477059048540), (341, 39651310, 4610693920140), (343, 40353093, 4747500979704), (345, 41063108, 4887536370360), (347, 41781403, 5030856893796), (349, 42508026, 5177520014100), (351, 43243025, 5327583861600), (353, 43986448, 5481107236704), (355, 44738343, 5638149613740), (357, 45498758, 5798771144796), (359, 46267741, 5963032663560), (361, 47045340, 6130995689160), (363, 47831603, 6302722430004), (365, 48626578, 6478275787620), (367, 49430313, 6657719360496), (369, 50242856, 6841117447920), (371, 51064255, 7028535053820), (373, 51894558, 7220037890604), (375, 52733813, 7415692383000), (377, 53582068, 7615565671896), (379, 54439371, 7819725618180), (381, 55305770, 8028240806580), (383, 56181313, 8241180549504), (385, 57066048, 8458614890880), (387, 57960023, 8680614609996), (389, 58863286, 8907251225340), (391, 59775885, 9138596998440), (393, 60697868, 9374724937704), (395, 61629283, 9615708802260), (397, 62570178, 9861623105796), (399, 63520601, 10112543120400), (401, 64480600, 10368544880400), (403, 65450223, 10629705186204), (405, 66429518, 10896101608140), (407, 67418533, 11167812490296), (409, 68417316, 11444916954360), (411, 69425915, 11727494903460), (413, 70444378, 12015627026004), (415, 71472753, 12309394799520), (417, 72511088, 12608880494496), (419, 73559431, 12914167178220), (421, 74617830, 13225338718620), (423, 75686333, 13542479788104), (425, 76764988, 13865675867400), (427, 77853843, 14195013249396), (429, 78952946, 14530579042980), (431, 80062345, 14872461176880), (433, 81182088, 15220748403504), (435, 82312223, 15575530302780), (437, 83452798, 15936897285996), (439, 84603861, 16304940599640), (441, 85765460, 16679752329240), (443, 86937643, 17061425403204), (445, 88120458, 17450053596660), (447, 89313953, 17845731535296), (449, 90518176, 18248554699200), (451, 91733175, 18658619426700), (453, 92958998, 19076022918204), (455, 94195693, 19500863240040), (457, 95443308, 19933239328296), (459, 96701891, 20373250992660), (461, 97971490, 20820998920260), (463, 99252153, 21276584679504), (465, 100543928, 21740110723920), (467, 101846863, 22211680395996), (469, 103161006, 22691397931020), (471, 104486405, 23179368460920), (473, 105823108, 23675698018104), (475, 107171163, 24180493539300), (477, 108530618, 24693862869396), (479, 109901521, 25215914765280), (481, 111283920, 25746758899680), (483, 112677863, 26286505865004), (485, 114083398, 26835267177180), (487, 115500573, 27393155279496), (489, 116929436, 27960283546440), (491, 118370035, 28536766287540), (493, 119822418, 29122718751204), (495, 121286633, 29718257128560), (497, 122762728, 30323498557296), (499, 124250751, 30938561125500), (501, 125750750, 31563563875500), (503, 127262773, 32198626807704), (505, 128786868, 32843870884440), (507, 130323083, 33499418033796), (509, 131871466, 34165391153460), (511, 133432065, 34841914114560), (513, 135004928, 35529111765504), (515, 136590103, 36227109935820), (517, 138187638, 36936035439996), (519, 139797581, 37656016081320), (521, 141419980, 38387180655720), (523, 143054883, 39129658955604), (525, 144702338, 39883581773700), (527, 146362393, 40649080906896), (529, 148035096, 41426289160080), (531, 149720495, 42215340349980), (533, 151418638, 43016369309004), (535, 153129573, 43829511889080), (537, 154853348, 44654904965496), (539, 156590011, 45492686440740), (541, 158339610, 46342995248340), (543, 160102193, 47205971356704), (545, 161877808, 48081755772960), (547, 163666503, 48970490546796), (549, 165468326, 49872318774300), (551, 167283325, 50787384601800), (553, 169111548, 51715833229704), (555, 170953043, 52657810916340), (557, 172807858, 53613464981796), (559, 174676041, 54582943811760), (561, 176557640, 55566396861360), (563, 178452703, 56563974659004), (565, 180361278, 57575828810220), (567, 182283413, 58602112001496), (569, 184219156, 59642978004120), (571, 186168555, 60698581678020), (573, 188131658, 61769078975604), (575, 190108513, 62854626945600), (577, 192099168, 63955383736896), (579, 194103671, 65071508602380), (581, 196122070, 66203161902780), (583, 198154413, 67350505110504), (585, 200200748, 68513700813480), (587, 202261123, 69692912718996), (589, 204335586, 70888305657540), (591, 206424185, 72100045586640), (593, 208526968, 73328299594704), (595, 210643983, 74573235904860), (597, 212775278, 75835023878796), (599, 214920901, 77113834020600), (601, 217080900, 78409837980600), (603, 219255323, 79723208559204), (605, 221444218, 81054119710740), (607, 223647633, 82402746547296), (609, 225865616, 83769265342560), (611, 228098215, 85153853535660), (613, 230345478, 86556689735004), (615, 232607453, 87977953722120), (617, 234884188, 89417826455496), (619, 237175731, 90876490074420), (621, 239482130, 92354127902820), (623, 241803433, 93850924453104), (625, 244139688, 95367065430000), (627, 246490943, 96902737734396), (629, 248857246, 98458129467180), (631, 251238645, 100033429933080), (633, 253635188, 101628829644504), (635, 256046923, 103244520325380), (637, 258473898, 104880694914996), (639, 260916161, 106537547571840), (641, 263373760, 108215273677440), (643, 265846743, 109914069840204), (645, 268335158, 111634133899260), (647, 270839053, 113375664928296), (649, 273358476, 115138863239400), (651, 275893475, 116923930386900), (653, 278444098, 118731069171204), (655, 281010393, 120560483642640), (657, 283592408, 122412379105296), (659, 286190191, 124286962120860), (661, 288803790, 126184440512460), (663, 291433253, 128105023368504), (665, 294078628, 130048921046520), (667, 296739963, 132016345176996), (669, 299417306, 134007508667220), (671, 302110705, 136022625705120), (673, 304820208, 138061911763104), (675, 307545863, 140125583601900), (677, 310287718, 142213859274396), (679, 313045821, 144326958129480), (681, 315820220, 146465100815880), (683, 318610963, 148628509286004), (685, 321418098, 150817406799780), (687, 324241673, 153032017928496), (689, 327081736, 155272568558640), (691, 329938335, 157539285895740), (693, 332811518, 159832398468204), (695, 335701333, 162152136131160), (697, 338607828, 164498730070296), (699, 341531051, 166872412805700), (701, 344471050, 169273418195700), (703, 347427873, 171701981440704), (705, 350401568, 174158339087040), (707, 353392183, 176642729030796), (709, 356399766, 179155390521660), (711, 359424365, 181696564166760), (713, 362466028, 184266491934504), (715, 365524803, 186865417158420), (717, 368600738, 189493584540996), (719, 371693881, 192151240157520), (721, 374804280, 194838631459920), (723, 377931983, 197556007280604), (725, 381077038, 200303617836300), (727, 384239493, 203081714731896), (729, 387419396, 205890550964280), (731, 390616795, 208730380926180), (733, 393831738, 211601460410004), (735, 397064273, 214504046611680), (737, 400314448, 217438398134496), (739, 403582311, 220404774992940), (741, 406867910, 223403438616540), (743, 410171293, 226434651853704), (745, 413492508, 229498678975560), (747, 416831603, 232595785679796), (749, 420188626, 235726239094500), (751, 423563625, 238890307782000), (753, 426956648, 242088261742704), (755, 430367743, 245320372418940), (757, 433796958, 248586912698796), (759, 437244341, 251888156919960), (761, 440709940, 255224380873560), (763, 444193803, 258595861808004), (765, 447695978, 262002878432820), (767, 451216513, 265445710922496), (769, 454755456, 268924640920320), (771, 458312855, 272439951542220), (773, 461888758, 275991927380604), (775, 465483213, 279580854508200), (777, 469096268, 283207020481896), (779, 472727971, 286870714346580), (781, 476378370, 290572226638980), (783, 480047513, 294311849391504), (785, 483735448, 298089876136080), (787, 487442223, 301906601907996), (789, 491167886, 305762323249740), (791, 494912485, 309657338214840), (793, 498676068, 313591946371704), (795, 502458683, 317566448807460), (797, 506260378, 321581148131796), (799, 510081201, 325636348480800), (801, 513921200, 329732355520800), (803, 517780423, 333869476452204), (805, 521658918, 338048020013340), (807, 525556733, 342268296484296), (809, 529473916, 346530617690760), (811, 533410515, 350835297007860), (813, 537366578, 355182649364004), (815, 541342153, 359572991244720), (817, 545337288, 364006640696496), (819, 549352031, 368483917330620), (821, 553386430, 373005142327020), (823, 557440533, 377570638438104), (825, 561514388, 382180729992600), (827, 565608043, 386835742899396), (829, 569721546, 391536004651380), (831, 573854945, 396281844329280), (833, 578008288, 401073592605504), (835, 582181623, 405911581747980), (837, 586374998, 410796145623996), (839, 590588461, 415727619704040), (841, 594822060, 420706341065640), (843, 599075843, 425732648397204), (845, 603349858, 430806882001860), (847, 607644153, 435929383801296), (849, 611958776, 441100497339600), (851, 616293775, 446320567787100), (853, 620649198, 451589941944204), (855, 625025093, 456908968245240), (857, 629421508, 462277996762296), (859, 633838491, 467697379209060), (861, 638276090, 473167468944660), (863, 642734353, 478688620977504), (865, 647213328, 484261191969120), (867, 651713063, 489885540237996), (869, 656233606, 495562025763420), (871, 660775005, 501291010189320), (873, 665337308, 507072856828104), (875, 669920563, 512907930664500), (877, 674524818, 518796598359396), (879, 679150121, 524739228253680), (881, 683796520, 530736190372080), (883, 688464063, 536787856427004), (885, 693152798, 542894599822380), (887, 697862773, 549056795657496), (889, 702594036, 555274820730840), (891, 707346635, 561549053543940), (893, 712120618, 567879874305204), (895, 716916033, 574267664933760), (897, 721732928, 580712809063296), (899, 726571351, 587215692045900), (901, 731431350, 593776700955900), (903, 736312973, 600396224593704), (905, 741216268, 607074653489640), (907, 746141283, 613812379907796), (909, 751088066, 620609797849860), (911, 756056665, 627467303058960), (913, 761047128, 634385293023504), (915, 766059503, 641364166981020), (917, 771093838, 648404325921996), (919, 776150181, 655506172593720), (921, 781228580, 662670111504120), (923, 786329083, 669896548925604), (925, 791451738, 677185892898900), (927, 796596593, 684538553236896), (929, 801763696, 691954941528480), (931, 806953095, 699435471142380), (933, 812164838, 706980557231004), (935, 817398973, 714590616734280), (937, 822655548, 722266068383496), (939, 827934611, 730007332705140), (941, 833236210, 737814832024740), (943, 838560393, 745688990470704), (945, 843907208, 753630233978160), (947, 849276703, 761638990292796), (949, 854668926, 769715688974700), (951, 860083925, 777860761402200), (953, 865521748, 786074640775704), (955, 870982443, 794357762121540), (957, 876466058, 802710562295796), (959, 881972641, 811133479988160), (961, 887502240, 819626955725760), (963, 893054903, 828191431877004), (965, 898630678, 836827352655420), (967, 904229613, 845535164123496), (969, 909851756, 854315314196520), (971, 915497155, 863168252646420), (973, 921165858, 872094431105604), (975, 926857913, 881094303070800), (977, 932573368, 890168323906896), (979, 938312271, 899316950850780), (981, 944074670, 908540643015180), (983, 949860613, 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