Congruum g : 400 <= g <= 499

Definition 1.

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

Definition 2.

(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

Type means,

1. m=i², n=j²
2. m=i², n=i²-j²
3. m=i²+j², n=i²
4. m=j², n=i²-j²
5. m=i²-j², n=j²

There are 36 congruum g : 400 <= g <= 499.
The solution of the following numbers are found.

437, 447, 469, 471

The solution of the following numbers are not in the range of 1 <= i, j <= 32,767.

407, 413, 415, 421, 431, 439, 446, 453,
454, 461, 463, 478, 479, 485, 487, 493

Congruum g : 400 <= g <= 499

g	m	n	x	y	z	type	i	j
406	3712	9	1507072	1850119264	3	(5)	61	3
410	81	1	33210	6051600	1	(1)	9	1
	81	40	3321	166419	2	(4)	11	9
	1369	640	56129	11755233	8	(2)	37	27
	17689	4000	725249	601634943	20	(2)	133	117
	10764961	531360	10764961	35276783759	36	(4)	3361	3281
	11296321	10233601	4631491610	133467323911200	3199	(1)	3361	3199
	66601921	64294560	66601921	141829031519	396	(2) (4)	8161 11441	1519 8161
422	685539	591361	289297458	2489074725480	769	(5)	1130	769
426	96	25	40896	7984944	5	(5)	11	5
	169	27	23998	3669848	3	(4)	14	13
	96845281	82473600	96845281	499581130321	440	(4)	13391	9841
	179318881	14371681	76389843306	21045251116169280	3791	(1)	13391	3791
	214476025	126997416	214476025	2531155204115	546	(4)	18479	14645
	341473441	87478609	145467685866	53630232292269360	9353	(1)	18479	9353
429	21025	6864	21025	2881585	4	(2) (4)	145 167	119 145
	27889	14161	11964381	35652422520	119	(1)	167	119
434	56	25	24304	3390408	5	(5)	9	5
	63	1	27342	4520544	1	(5)	8	1
	289	72	62713	15209747	6	(4)	19	17
	361	217	722	15504	1	(2)	19	12
	22801	12168	4947817	9307564651	78	(4)	187	151
	34969	10633	69938	17619888	7	(2)	187	156
	2353400	1771561	1021375600	21487891692120	1331	(5)	2031	1331
	3940225	249984	3940225	7805589695	24	(2) (4)	1985 2047	1921 1985
	4190209	3690241	1818550706	36736607664960	1921	(1)	2047	1921
	10435887	9778129	4529174958	106502217463488	3127	(5)	4496	3127
	14145121	14061600	14145121	5772679919	180	(2) (4)	3761 5311	289 3761
437	79459396	29545171	1827566108	72526863610530	1247	(2)	8914	7065
438	49	24	3577	186515	2	(2)	7	5
	8862529	8584800	8862529	6553207583	140	(4)	4177	2977
	17447329	277729	7641930102	667958625341280	527	(1)	4177	527
442	121	104	2057	47685	2	(4)	15	11
	729	104	12393	1365525	2	(2)	27	25
	841	9	371722	226622240	3	(1)	29	3
	12299049	362024	209083833	3021986055795	118	(2)	3507	3455
	32684089	13461561	14446367338	1582239532440320	3669	(1)	5717	3669
	648058849	192535200	648058849	15752730477743	660	(2)	25457	21343
445	169	9	75205	20594600	3	(1)	13	3
	205091041	43318080	205091041	2870847221039	312	(4)	15761	14321
447	503643364	461433361	225128583708	42806671029093510	21481	(1)	22442	21481
455	64	1	29120	4968600	1	(1)	8	1
	16785409	1048320	16785409	68635570177	48	(2)	4097	3967
	17833729	15737089	8114346695	343859535146400	3967	(1)	4223	3967
457	64009	41616	29252113	120208263175	204	(1) (5) (4)	253 325 325	204 204 253
	107497825	1016064	49126506025	10888158024855595	1008	(5)	10417	1008
	108513889	106481761	49590847273	2127195133066080	10319	(1)	10417	10319
462	100489	46200	100489	28288763	10	(2) (4)	317 383	233 317
	146689	54289	67770318	518288989680	233	(1)	383	233
465	16	15	496	3844	1	(2)	4	1
	841	4	391065	244550475	2	(1)	29	2
	17161	1444	7979865	22462101675	38	(1)	131	38
	231361	29760	231361	110360159	8	(2) (4)	481 511	449 481
	261121	201601	121421265	850338543600	449	(1)	511	449
	686020864	683640015	21266646784	258156850806352	6751	(2)	26192	1543
	901020289	44111760	901020289	27013494147263	308	(2) (4)	30017 30743	29273 30017
469	1467568	1212201	688289392	10178632806076	1101	(5)	1637	1101
470	49	45	4606	123704	3	(2)	7	2
471	152942689	129846025	72036006519	10216482282479772	11395	(1)	12367	11395

• 1 <= ‚‡ <= 99
• 100 <= ‚‡ <= 199
• 200 <= ‚‡ <= 299
• 300 <= ‚‡ <= 399
• 400 <= ‚‡ <= 499
• 500 <= ‚‡ <= 599
• 600 <= ‚‡ <= 699
• 700 <= ‚‡ <= 799
• 800 <= ‚‡ <= 899
• 900 <= ‚‡ <= 999