### Congruum g : 1 <= g <= 999

Definition 1.

k2g=mn(m2-n2)
k, m, n, g in N (integer > 0)

Definition 2.

x2+gy2=z2
x2-gy2=w2

x, y, z, w in N (integer > 0)

m=x2, n=gy2

Definition 3.

(x/z2, y/z3) on elliptic curve Y2=X3-g2X
x, y, z in Z (integer)
X, Y in Q (rational)

X=mg/n, Y=kg2/n2

We are using the same characters x, y, z in the definition 2 and 3,
but I think there's no confusion.

There are 361 congruent numbers in the range of 1 <= g <= 999.

```g, m, n

5, 5, 4
6, 2, 1
7, 16, 9
13, 325, 36
14, 8, 1
15, 4, 1
21, 4, 3
22, 50, 49
23, 24336, 17689
29, 4901, 4900
30, 3, 2
31, 1600, 81
34, 9, 8
37, 777925, 1764
38, 1250, 289
39, 13, 12,
41, 25, 16,
46, 72, 49,
47, 14561856, 2289169,
53, 1873180325, 1158313156,
55, 125, 44,
61, 12079525, 10227204
62, 39200, 22801,
65, 9, 4,
69, 192, 169,
70, 7, 2,
71, 3600, 121,
77, 2816, 2809,
78, 26, 1,
79, 169000000, 166952241,
85, 85, 36,
86, 338, 49
87, 17956, 169
93, 1444, 75
94, 14112, 529
95, 1445, 76
101, 44715091781, 3975302500
102, 50, 1
103, 8780605285453456, 7551929273974569
109, 2725, 1764
110, 10, 1
111, 37, 12
118, 716311250, 19298449
119, 144, 25
127, 306317326339867638016, 305111826865145547009
133, 256036, 143811
134, 2084882, 14161
137, 3425, 3136
138, 24, 1
141, 48, 1
142, 4918336200, 164070481
143, 101124, 1849
145, 29, 20
149, 93125, 56644
151, 115600, 35721
154, 9, 2
157, 443624018997429899709925, 166136231668185267540804
158, 768800, 579121
159, 33124, 11449
161, 16, 7
165, 16, 11
166, 197646962, 96020401
167, 115222229136, 3447686089
173, 2404644000341688241925, 2367961190733987384484
174, 27, 2
181, 3073858021, 1221502500
182, 343, 18
183, 17853541, 456300
190, 10, 9
191, 404727588018561600, 384957657745092721
194, 97, 72
197, 1991322221917925, 103880003159716
199, 13933945152400, 27368486201
205, 45, 4
206, 3886472, 1216609
210, 5, 2
213, 7680000, 724201
214, 195938, 82369
215, 3844, 361
219, 73, 48
221, 13, 4
222, 12506, 3481
223, 50942322536708571136, 14384824876061849889
226, 81, 32
229, 874407840421, 7574220900
230, 1127, 722
231, 7, 4
237, 1888250116, 104961675
238, 1800, 1681
239, 14400, 14161
246, 578, 529
247, 35976004, 34539129
253, 125316, 91091
254, 147968, 25921
255, 16, 1
257, 23409, 10816
262, 107898050, 91259809
263, 2415046965407199886472444395015056, 2196589972531420851340521356470969
265, 49, 4
269, 1973658180741549394113125, 6841040196454710370084
271, 90565100276929600, 10384564009711761
277, 14983858080745346212342049973925, 1065773764946955463053657843204
278, 983320808450, 981718327489
285, 76, 49
286, 11, 2
287, 19017513216, 19017237409
291, 49, 48
293, 15705303325706301534145925, 14764613336211576651809284
295, 937445, 226796
299, 36, 13
301, 2752, 729
302, 9398643356699544200, 9025426439116032001
303, 40822586116, 27689958409
309, 11957764, 1915203
310, 40, 9
311, 190727483528715254643600, 124670583817928357228041
313, 169, 144
317, 2761253095084587196325, 283607850589557281956
318, 1083, 242
319, 2500, 2401
323, 425, 304
326, 2266125842, 461041
327, 6922040749, 6897607500
330, 6, 5
334, 3274885399752, 1127604000769
335, 7828804, 6911641
341, 13924, 2475
349, 19385975941, 12934512900
353, 289, 64
357, 21, 4
358, 956307324451250, 419801702617969
359, 3302812394010000, 3302771130607081
365, 80957528885, 9001075876
366, 122, 121
367, 268375455300992413724915588959538171729183296, 246962909981075733725521615532807811435729
371, 53, 28
373, 2528397723062320973179188676827215493925, 268218643743370556175474368869395176964
374, 1682, 1
381, 158404, 146523
382, 33312967200, 7863965041
383, 403654067228736, 303839168346289
386, 121, 72
389, 84049783723809350326254513125, 5237316101673450088070309764
390, 8, 5
391, 327184, 308025
395, 80, 1
397, 4720652373925, 4280901693156
398, 860278445000, 650976262561
399, 64, 57
406, 3712, 9
407, 4662023125, 4661617356
410, 41, 40
413, 4110604996, 2277480771
415, 881971204, 245580241
421, 452568163984303525, 36031587602493924
422, 638450, 47089
426, 96, 25
429, 12, 1
430, 3483, 3362
431, 193276189912334400, 3177076466844721
434, 32, 31
437, 79459396, 29545171
438, 49, 24
439, 70989410337024400, 43044356506452921
442, 121, 104
445, 89, 80
446, 2835884807783552, 377414273685409
447, 503643364, 461433361
453, 1708547008996, 1567254468675
454, 1002780063842, 856940855521
455, 64, 1
457, 64009, 41616
461, 50724269719704638882388101, 36304957961648911912322500
462, 14, 11
463, 1162623700824087616, 141856298295251409
465, 16, 15
469, 1467568, 1212201
470, 47, 2
471, 141394357, 11548332
478, 115925065606428893644500000, 1634220262284462674687761
479, 2145542400, 522076801
485, 19921511285, 6611966596
487, 1019034345734453406615667216, 409136538889385517944610009
493, 59747170703125, 9162402086916
494, 2299, 1458
501, 239341872, 17330569
502, 347052959946050, 33057359699809
503, 15881569125140359780032984660061332598637667216, 15492409457317760025384676078081128557650708009
505, 101, 20
509, 86021, 28900
510, 32, 17
511, 359178304, 4601025
514, 257, 32
517, 36, 11
518, 1184, 841
519, 326025012196, 4124593729
526, 28486152, 18769
527, 576, 49
533, 19348233125, 18912300484
534, 49298, 47089
535, 174724, 96721
541, 3695829951343408861029541, 2655840753566898560252100
542, 139028384968680306034023200, 36879659147456455555864081
543, 130750714824264730429, 27089515171392307500
546, 7, 6
551, 122500, 32041
557, 1698956704241831560325, 1616556585387687403684
559, 2608225, 4489
561, 17, 16
565, 949765, 311364
566, 19462073861042, 258756359761
573, 72524591339947200, 49616483059370929
574, 288, 1
581, 306916, 269667
582, 194, 169
583, 4127673125, 4045752524
589, 16931584, 5130225
590, 16810, 4489
591, 1976836, 32761
597, 20332217085474456484, 12746213318246067075
598, 899496, 528529
599, 3038870911771011886354576369729571392520234010000, 1684988316181288974002607111763585731071026338361
602, 25, 18
606, 2187, 338
607, 125293941159013578901968618425335451919780530015678850455884723272256, 28106647023546616494565410735723361950369596834744611141477253594769
609, 25, 4
613, 134258586449534325996866004325, 2167741978776656970024461796
614, 7188810031138898, 3271718393929969
615, 484, 361
622, 16200, 961
623, 9246113759335228416, 917852707195412209
629, 629, 100
631, 7121391825113218180095235600, 7063072218419717533435319241
638, 44839971, 38281250
645, 125, 4
646, 18, 1
647, 1322160612567067320518390399934355553879100499050449996991864027974293776, 582675374825367622310345719733993297770816424257895824163140848520889449
651, 28, 3
653, 16039906351002089646726601004613956083758645547269701746398265925, 14182059891839277799515376046557567884269244616864333585635276676
654, 36842, 14641
655, 250986125, 4150604
658, 128, 47
661, 1827011937314914952625145627525, 1788754861111702406537568159684
662, 3964067407661153562050, 2971995056622029919649
663, 325, 204
669, 196, 27
670, 603, 242
671, 36, 25
674, 337, 288
677, 47927715455890725716869695510411087930312812511079044688038242680325, 37092798385418402372420837363147418226160953779371767824311918038756
678, 7106450, 6589489
679, 23324765703184, 22433058686025
685, 101380695056485, 14140593118404
687, 7502269, 410700
689, 689, 400
694, 144722, 108241
695, 57924313445, 26709551116
701, 424441571475461208113369493075504899525, 415387564510365861372968392912738762084
703, 1384862947204, 774007569729
709, 204901, 44100
710, 1440, 1369
717, 5402982087403200, 442947484849
718, 40949496158275253352971518245000, 6499888481560323372961451565601
719, 350438400, 272613121
721, 112, 9
723, 10609, 1200
727, 262866283445837565478197874923005550901524713509432228282087904339282031376, 134743807384934886048168596694816992039931007003491174422071019408679945849
731, 1521, 688
733, 42202047131581996388978204646062320777476945363051718065925, 30875705726293957067602327680955336278845752827135827134404
734, 829472, 18769
741, 16, 3
742, 1991056936, 675116289
743, 442081912085141580068205924381130314284533683543584687891856, 4923545999394502506171933125524998796854945340571916996169
749, 207152, 94249
751, 270400, 53361
757, 13602273107694756028798442021854633219790498492407291327120413272088837819189925, 6244756715574614879455468252566469219452570766747039517820858029581943762708004
758, 29448487134996834815262304148851250, 186062309862174127714929896033329
759, 12, 11
761, 640001, 1600
766, 691932401810510112, 23501280303420529
767, 211010428335204, 14971660478329
773, 989084230222373972333910805925, 395556919548784859614258538116
777, 148, 27
781, 4324112302500, 3683537773619
782, 24200, 5041
789, 8489443248, 6945388921
790, 77440, 1521
791, 113, 112
793, 19825, 17424
797, 33774422602919140585730411489969262195586409011795565639723428586290973904287392325, 5996643567874741587549707954567755873065370996868154128163410594841412962150844516
798, 32, 25
799, 64, 17
805, 81, 80
806, 31, 18
807, 415681879805284, 40681805176441
813, 196, 75
814, 74, 25
815, 4007741050385284, 3642335055801121
821, 672419525, 37429924
822, 63685236050, 49283556001
823, 3242635455264585956601518619150703534549412676347725149402642778377509709168016, 1195374870805855749961759118845148692286556133409866986910805318758576537878009
829, 1030055240843789503113650334926694761339101122026725, 177750573637318822104546934614413436162693927477444
830, 6723, 1682
831, 6650436108390733, 529824935498508
838, 128300399536533744621494450, 3013299452291575001275249
839, 921024090000, 798612109801
853, 2063644701214713560377801387332325, 1714573714638475303870575201815556
854, 11767, 1458
861, 2541, 2500
862, 2016643668909039569085152743098413287200, 1974330716960706704228129795667231395761
863, 1865955041348432071713419570491743304896576, 1858782575121402159177467199382221005546449
866, 361, 72
869, 475904, 286225
870, 145, 24
871, 13293316, 12809241
877, 8426023978582911503830444690267601350433831421925, 81307125890381364089453146670538087002747953764
878, 4892629929800, 4646443224721
879, 3844, 3481
885, 399424, 205379
886, 6568985816978, 4971575468209
887, 4536847899397194814782383112783728104152935409787863620887731098256, 376228287896231431732378232468716810769990224188408143567460976969
889, 64, 63
890, 49, 40
893, 98976113486833636, 3224135528266411
894, 1391283, 10658
895, 142805, 86636
901, 2873, 848
902, 5281250, 5276209
903, 172, 3
905, 181, 180
910, 65, 56
911, 10337603501168361479121072317589371823133263769269309465600, 10251038973842988792231450622875404412229672018176136927201
915, 61, 60
917, 6243557649986596, 1330622224234371
919, 172438957409290000, 94730381860226121
926, 86485853224649872668557955872, 4336954975876583369002712209
933, 1180457237875251598830000, 821142362599087465303081
934, 37538, 289
935, 2704, 2209
941, 45445208211554090721215702021, 45093936839814465880092660100
942, 1673306, 1190281
943, 34481, 9200
949, 949, 900
951, 196, 121
957, 29, 4
958, 8227224286063797798196820892172800, 7536459073489487535964603134454081
959, 5184, 4225
965, 1368547063155978485, 72225290780597956
966, 23, 2
967, 1669158917895536251704589403770563104478686864745616, 991936373451122630263885658159644238540608455699609
973, 5476, 1251
974, 2927411969212856264181512, 129458146762062069194929
982, 22599162783624879100060329302450, 1855038663733663467087769013329
983, 34499614166703093964327810353786154232194081202481758752971756816, 27595011125826459222677977624378565666052727191819391300400129209
985, 26569, 6724
987, 336, 289
989, 44548856356, 23518926067
991, 139113978859943328654400, 126099694516817139337521
995, 320, 121
997, 42213709768307514171686429890363488527317316427348844504307265329655015861152197726745537308248325, 3761555284456864241854415331157386556136120253716483379037244121900171126528942748431935644922916
998, 99017507481041765919078929839247234450, 45684092521200925325386025716112737489
```

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E-mail : kc2h-msm@asahi-net.or.jp
Hisanori Mishima