Congruum g : 1 <= g <= 99

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

There are 36 congruum g : 1 <= g <= 99.
The solution of the following numbers are not in the range of 1 <= m, n <= 1,000,000.

47, 53, 61, 79

Congruum g : 1 <= g <= 99

g	m	n	x	y	z
5	5	4	25	75	2
	1681	720	1681	62279	12
6	2	1	12	36	1
	25	24	25	35	2
	2738	529	16428	2065932	23
7	16	9	112	980	3
	113569	100800	113569	17631503	120
13	325	36	4225	272935	6
14	8	1	112	1176	1
	4225	2016	4225	241345	12
15	4	1	60	450	1
	289	240	289	2737	4
	487204	450241	7308060	7548294150	671
21	4	3	28	98	1
	625	336	625	13175	4
22	50	49	1100	7260	7
23	24336	17689	559728	287596140	133
29	4901	4900	142129	1082367	70
30	3	2	45	225	1
	169	120	169	1547	2
	186003	242	2790045	4660327575	11
31	1600	81	49600	11032280	9
34	9	8	153	867	2
	17	8	289	4335	2
	49	32	833	18207	4
	961	128	16337	2069529	8
	21025	4896	21025	2964815	12
	28577	1352	485809	338229705	26
	124609	122400	124609	8245727	60
	131769	2888	2240073	3351883557	38
37	777925	1764	28783225	154421605115	42
38	1250	289	47500	10071900	17
39	13	12	169	845	2
	97969	15600	97969	30273047	20
41	25	16	1025	25215	4
	441	400	18081	1023729	20
	1025	64	42025	8598315	8
	296225	135424	12145225	37644053445	368
	776161	590400	776161	443882159	120
46	72	49	3312	139656	7
55	125	44	625	14625	2
62	39200	22801	2430400	3082042320	151
65	9	4	585	12675	2
	65	16	4225	266175	4
	121	4	7865	697125	2
	3481	3364	226265	27669525	58
	9409	9360	9409	93023	12
	18785	12544	1221025	1004328975	112
69	192	169	13248	723672	13
70	7	2	245	3675	1
	2809	2520	2809	65773	6
71	3600	121	255600	129150420	11
77	2816	2809	216832	7114800	53
78	26	1	2028	91260	1
	458329	70200	458329	306627517	30
85	85	36	7225	556325	6
86	338	49	29068	4903548	7
87	17956	169	1562172	1952423550	13
93	1444	75	44764	9458162	5
94	14112	529	1326528	1526754768	23
95	1445	76	7225	613275	2

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