Congruum g : 300 <= g <= 399

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 39 congruum g : 300 <= g <= 399.
The solution of the following numbers are found.

309, 335

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

302, 303, 311, 317, 326, 327, 334, 349, 358,
359, 365, 367, 373, 382, 383, 389, 397, 398

Congruum g : 300 <= g <= 399

g	m	n	x	y	z	type	i	j
301	2752	729	828352	726982424	27	(5)	59	27
309	11957764	1915203	1231649692	42666571062206	799	(2)	3458	3169
310	40	9	12400	1345400	3	(5)	7	3
	2825761	2187360	2825761	3007243441	84	(4)	2239	1681
	5013121	638401	1554067510	60765136303200	799	(1)	2239	799
313	169	144	52897	6367985	12	(3) (2) (1)	12 13 13	5 5 12
318	1325	841	421350	211349160	29	(3)	29	22
319	2500	2401	797500	198433950	49	(1)	50	49
323	529	304	8993	697935	4	(2)	23	15
	729	121	235467	112675320	11	(1)	27	11
	91809	1216	1560753	1949679255	8	(4)	305	303
	1096209	822016	18635553	53222836785	208	(4)	1385	1047
330	3721	1320	3721	212219	2	(2) (4)	61 71	49 61
	5041	2401	1663530	1886583600	49	(1)	71	49
	5329	5280	5329	52633	4	(2) (4)	73 103	7 73
	10609	49	3500970	6550552800	7	(1)	103	7
	1471369	582120	1471369	1639149947	42	(4)	1433	1213
	488100649	273273000	488100649	8935085267893	910	(2)	22093	14657
335	7828804	6911641	2622649340	63080260933950	2629	(1)	2798	2629
341	13924	2475	431644	279072478	15	(2)	118	107
353	289	64	102017	31775295	8	(1) (2)	17 17	8 15
357	21	4	7497	637245	2	(5)	5	2
	208849	142800	208849	69647257	20	(2) (4)	457 593	257 457
	351649	66049	125538693	1381552257960	257	(1)	593	257
366	122	121	44652	1205604	11	(3)	11	1
	871725625	14348664	871725625	25734212234675	198	(2) (4)	29525 29767	29281 29525
371	81	25	30051	4955076	5	(1)	9	5
	484	477	3388	33418	3	(4)	31	22
	3392	1369	1258432	1291623144	37	(5)	69	37
	448592	100489	166427632	2092467482196	317	(5)	741	317
	12909649	12020400	12909649	16917277607	180	(4)	4993	3593
374	1683	1681	629442	24338424	41	(5)	58	41
381	158404	146523	20117308	34285705622	221	(2)	398	109
386	121	72	23353	2868173	6	(2)	11	7
	1651225	405769	637372850	15597851874480	637	(1) (2)	1285 1285	637 1116
	8994001	7465248	1735842193	40335374922823	1932	(4)	4057	2999
	393030625	329557536	393030625	4245740377775	924	(4)	26881	19825
	722588161	63473089	278919030146	146735498931621600	7967	(1)	26881	7967
390	7921	6240	7921	434231	4	(2) (4)	89 119	41 89
	14161	1681	5522790	12887128800	41	(1)	119	41
391	327184	308025	127928944	487872012628	555	(1) (5) (4)	572 797 797	555 555 572
395	80	1	31600	5616900	1	(5)	9	1
	77841	1369	30747195	170467298100	37	(1)	279	37
	91204	91125	7205116	804801914	135	(4)	427	302
	40972801	2047680	40972801	261939168001	72	(2) (4)	6401 6559	6239 6401
	43020481	38925121	16993089995	943283290748400	6239	(1)	6559	6239
	112741924	100038645	8906611996	387620965667006	4473	(4)	14587	10618
399	64	57	448	4312	1	(4)	11	8
	53949025	12359424	53949025	385716850415	176	(2)	7345	6449
	66308449	41589601	26457071151	3351696530101920	6449	(1)	8143	6449

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