Congruum g : 500 <= g <= 599

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 37 congruum g : 500 <= g <= 599.
The solution of the following numbers are found.

511, 526, 559, 589, 591

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

501, 502, 503, 519, 533, 541, 542,
543, 557, 566, 573, 583, 597, 599

Congruum g : 500 <= g <= 599

g	m	n	x	y	z	type	i	j
505	121	81	61105	11221100	9	(1)	11	9
	85345	28224	43099225	267026221475	168	(5)	337	168
	316969	25281	160069345	2018721794500	159	(1)	563	159
	112381201	79192080	112381201	845302548601	396	(4)	13841	10601
509	86021	28900	43784689	272883022113	170	(5)	339	170
510	49	15	1666	64736	1	(4)	8	7
	1723969	1599360	1723969	844940447	56	(4)	1823	1313
	3323329	124609	1694897790	69728411188800	353	(1)	1823	353
511	359178304	4601025	183540113344	78625036156344328	2145	(5) (4)	19073 19073	2145 18952
514	289	225	148546	35930656	15	(3) (2) (1)	15 17 17	8 8 15
	938961	430592	241312977	3331213084569	464	(2)	969	713
	27804529	24165152	7145763953	298776203813367	3476	(4)	7209	5273
517	36	11	1692	66270	1	(2)	6	5
	2007889	1861200	2007889	1067512537	60	(2) (4)	1417 1967	383 1417
518	1184	841	613312	338088240	29	(5)	45	29
526	28486152	18769	14983715952	1834126150387944	137	(5)	5339	137
	28504921	28467383	57009842	22083727056	329	(4)	7548	5339
527	576	49	303552	166637400	7	(1) (5) (4)	24 25 25	7 7 24
534	49298	47089	26325132	39979156356	217	(3)	217	47
	96387	2209	51470658	369169231032	47	(5)	314	47
535	174724	96721	93477340	752668136550	311	(1)	418	311
546	39	25	21294	2384928	5	(5)	8	5
	975	961	532350	65585520	31	(5)	44	31
	7225	2184	7225	585395	2	(2) (4)	85 97	71 85
	9409	5041	5137314	9831865680	71	(1)	97	71
	133225	19656	133225	48094955	6	(2) (4)	365 391	337 365
	152881	113569	83473026	510547499280	337	(1)	391	337
	1151329	873600	1151329	804665233	40	(4)	1423	1073
	2024929	277729	1105611234	36414964797120	527	(1)	1423	527
	116049375	9480241	63362958750	15896414754183600	3079	(5)	11204	3079
551	122500	32041	67497500	535233382950	179	(1)	350	179
559	2608225	4489	1457997775	55671721203540	67	(1)	1615	67
561	17	16	9537	314721	4	(3)	4	1
	33	16	18513	2203047	4	(5)	7	4
	361	64	202521	89695485	8	(1)	19	8
	1849	1024	1037289	879645195	32	(1)	43	32
	297025	35904	297025	160691615	8	(2) (4)	545 577	511 545
	1553937	1373584	871758657	12035737040481	1172	(5)	1711	1172
	1809025	1759296	1809025	566577215	56	(4)	1889	1345
565	949765	311364	536617225	11743763263325	558	(5)	1123	558
574	288	1	165312	67213104	1	(5)	17	1
	289	287	578	1632	1	(4)	24	17
581	306916	269667	2148412	1503644086	57	(2)	554	193
582	194	169	112908	18629820	13	(3)	13	5
589	16931584	5130225	9972702976	949091989929776	2265	(5)	4697	2265
591	1976836	32761	1168310076	39927998137230	181	(1)	1406	181
598	899496	528529	537898608	10094549417160	727	(5)	1195	727

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