Congruum g : 600 <= g <= 699

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 35 congruum g : 600 <= g <= 699.
The solution of the following numbers are found.

655, 678, 687

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

607, 613, 614, 623, 631, 638, 647,
653, 661, 662, 677, 679, 685, 695

Congruum g : 600 <= g <= 699

g	m	n	x	y	z	type	i	j
602	41624	39601	25057648	38628642360	199	(5)	285	199
	205209	181675	2872926	2264271576	65	(4)	622	453
	900601	541800	900601	682709651	30	(4)	1201	949
	1442401	358801	868325402	24782975795760	599	(1)	1201	599
	20820969	10966075	291493566	4230518246136	505	(4)	5638	4563
606	2525	1849	1530150	1288998360	43	(3)	43	26
609	25	4	15225	1854405	2	(1)	5	2
	256	87	1792	71344	1	(2)	16	13
	1936	87	13552	1576036	1	(2)	44	43
	410881	243600	410881	212094721	20	(2) (4)	641 809	409 641
	616225	87696	616225	478813105	12	(2) (4)	785 839	727 785
	2105401	1188100	1282189209	37903401397323	1090	(1)	1451	1090
615	484	361	297660	108172350	19	(1)	22	19
622	16200	961	10076400	31929536520	31	(5)	131	31
	17161	15239	34322	2923920	7	(4)	180	131
629	629	100	395641	245693061	10	(5)	27	10
645	244640881	31218000	244640881	3795146019721	220	(2)	15641	14609
646	105625	23256	105625	33485725	6	(2) (4)	325 359	287 325
	128881	82369	83257126	584284131600	287	(1)	359	287
651	169	48	36673	6733727	4	(2)	13	11
	2116	93	14812	1800946	1	(4)	47	46
	11236	7533	78652	16366294	9	(4)	137	106
	628849	260400	628849	453913993	20	(2) (4)	793 943	607 793
	20967241	292032	4549891297	306873511545041	312	(2)	4579	4547
655	255136729	246835521	167114557495	17284584503894500	15711	(1)	15973	15711
658	175	81	115150	34637120	9	(5)	16	9
	529	200	174041	67217661	10	(4)	27	23
	729	329	1458	49680	1	(2)	27	20
	4536	4489	2984688	740368440	67	(5)	95	67
	1310904	121	862574832	25333498645560	11	(5)	1145	11
	345699649	341107200	345699649	1044212647393	720	(2)	18593	2143
663	529	121	350727	202201740	11	(1)	23	11
669	196	27	43708	9050678	3	(2)	14	13
671	36	25	24156	2701446	5	(1)	6	5
	3690241	2415600	3690241	5359127039	60	(2)	1921	1129
674	625	49	421250	272565600	7	(1) (2)	25 25	7 24
	543169	23328	183047953	2474266135033	108	(2)	737	721
	566497	519841	381818978	2965001304672	721	(3)	721	216
	4464769	2765952	1504627153	45815080051943	1176	(4)	2689	2113
678	7106450	6589489	4818173100	125226340712460	2567	(3)	2567	719
	13695939	516961	9285846642	894175289593560	719	(5)	3770	719
687	7912969	7091569	5436209703	177825279870180	2663	(1)	2813	2663
689	689	400	474721	266318481	20	(3) (5)	20 33	17 20
	21609	9025	14888601	52198422276	95	(1)	147	95
	34969	625	24093641	118245405564	25	(1)	187	25
694	144722	108241	100437068	668141353188	329	(3)	329	191
	252963	36481	175556322	2301764452344	191	(5)	538	191

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