Congruum g : 100 <= g <= 199

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 : 100 <= g <= 199.
The solution of the following numbers are found.

134, 166, 183

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

101, 103, 118, 127, 142, 157,
167, 173, 181, 191, 197, 199

Congruum g : 100 <= g <= 199

g	m	n	x	y	z	type	i	j
102	51	49	5202	104040	7	(5)	10	7
	6255001	499800	6255001	15593737501	70	(2)	2501	2399
	6754801	5755201	688989702	9467784199440	2399	(1)	2599	2399
109	2725	1764	297025	123384185	42	(3) (5)	42 67	31 42
	4489	961	489301	334331340	31	(1)	67	31
110	10201	3960	10201	949501	6	(2) (4)	101 119	79 101
	14161	6241	1557710	1745158800	79	(1)	119	79
111	49	25	5439	344988	5	(1)	7	5
	2289169	2175600	2289169	1077378553	140	(4)	2113	1513
	4464769	113569	495589359	11029159413720	337	(1)	2113	337
119	144	25	17136	2209116	5	(1) (5) (4)	12 13 13	5 5 12
	456292321	289598400	456292321	7532151788881	1560	(2)	21361	12911
	745890721	166693921	88760995799	25775535638208720	12911	(1)	27311	12911
133	256036	143811	1792252	1985131610	87	(2)	506	335
134	2099043	2070721	281271762	772299159576	1439	(5)	2042	1439
137	3425	3136	469225	129224565	56	(3) (5)	56 81	17 56
	6561	289	898857	851361840	17	(1)	81	17
	38809	784	5316833	12257189295	28	(1) (2)	197 197	28 195
	1375929	1073296	188502273	1619389601535	1036	(1) (5) (4)	1173 1565 1565	1036 1036 1173
138	24	1	3312	190440	1	(5)	5	1
	121	75	5566	325864	5	(4)	14	11
	3721	3675	171166	11100536	35	(4)	86	61
	259584	143641	35822592	178588537920	379	(5)	635	379
	332929	55200	332929	189441217	20	(2) (4)	577 623	527 577
	388129	277729	53561802	273830628960	527	(1)	623	527
	395641	124200	395641	236278189	30	(2) (4)	629 721	521 629
	519841	271441	71738058	518197523760	521	(1)	721	521
	102677689	81820200	102677689	628586073613	770	(2)	10133	4567
141	48	1	6768	556668	1	(5)	7	1
	5755201	4870849	811483341	12312817025040	2207	(1)	2399	2207
143	101124	1849	14460732	54981021810	43	(1)	318	43
145	49	9	7105	588700	3	(1)	7	3
	145	144	21025	357425	12	(3) (5)	12 17	1 12
	289	1	41905	8578200	1	(1)	17	1
	961	729	139345	33892300	27	(1)	31	27
	73441	45369	10648945	27326528900	213	(1)	271	213
	1540081	1023120	1540081	1428538679	84	(4)	1601	1241
	2563201	516961	371664145	7017919780200	719	(1)	1601	719
	4962625	1272384	719580625	18657508153625	1128	(5)	2497	1128
	6235009	3690241	904076305	21911160018000	1921	(1)	2497	1921
149	93125	56644	13875625	41025782925	238	(3) (5)	238 387	191 238
	149769	36481	22315581	102242265300	191	(1)	387	191
151	115600	35721	17455600	69360185980	189	(1) (5) (4)	340 389 389	189 189 340
154	25	11	350	5880	1	(4)	6	5
	88	81	13552	616616	9	(5)	13	9
	352	9	54208	12616912	3	(5)	19	3
	7225	5544	7225	393805	6	(2) (4)	85 113	41 85
	12769	1681	1966426	2733506160	41	(1)	113	41
	94249	6875	1319486	1511640984	25	(4)	318	307
	139129	138600	139129	4521133	30	(2) (4)	373 527	23 373
	277729	529	42770266	279712670160	23	(1)	527	23
	619369	508475	8671166	14579590536	215	(4)	1062	787
	204633025	33729696	204633025	2887236042335	468	(4)	15439	14305
158	768800	579121	121470400	880509737520	761	(5)	1161	761
	1347921	189679	2695842	4382264160	49	(4)	1240	1161
159	33124	11449	5266716	11341815030	107	(1)	182	107
161	16	7	368	6348	1	(2)	4	3
	225	64	36225	6609855	8	(1) (5) (4)	15 17 17	8 8 15
	368	361	59248	2799468	19	(5)	27	19
	44528	841	7169008	19191597348	29	(5)	213	29
	93025	92736	93025	2234735	24	(2) (4)	305 431	17 305
	185761	289	29907521	163557362640	17	(1)	431	17
	314721	160000	50670081	310595764479	400	(1) (5) (4)	561 689 689	400 400 561
165	142129	95040	142129	39840983	24	(2) (4)	377 487	217 377
	237169	47089	39132885	239927173200	217	(1)	487	217
166	293667363	101626561	48748782258	10098265824004248	10081	(5)	19882	10081
174	29	25	5046	181656	5	(3)	5	2
	537289	156600	537289	376733413	30	(2) (4)	733 833	617 733
	693889	380689	120736686	1109171553840	617	(1)	833	617
182	361	325	5054	156408	5	(2)	19	6
183	18309841	17397241	3350700903	60469493893380	4171	(1)	4279	4171
190	10	9	1900	36100	3	(3)	3	1
	32761	6840	32761	5799059	6	(2) (4)	181 199	161 181
	39601	25921	7524190	15603430800	161	(1)	199	161
194	169	25	32786	5871216	5	(1) (2)	13 13	5 12
	5041	288	488977	341367929	12	(4)	73	71
	5329	4753	10658	497568	7	(2)	73	24
	19321	8712	1874137	2290047101	66	(2)	139	103
	13446889	12882888	1304348233	13499946232613	2538	(2)	3667	751
	212955649	118029600	212955649	2586673444607	780	(2)	14593	9743

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