Congruum g : 200 <= g <= 299

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 : 200 <= g <= 299.
The solution of the following numbers are found.

206, 213, 247, 262

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

223, 229, 237, 263, 269, 271, 277, 278, 287, 293

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Congruum g : 200 <= g <= 299

g	m	n	x	y	z	type	i	j
205	45	4	9225	882525	2	(5)	7	2
	4165681	1446480	4165681	7973127721	84	(2) (4)	2041 2369	1649 2041
	5612161	2719201	1150493005	34136977765800	1649	(1)	2369	1649
206	3886472	1216609	800613232	21514899485016	1103	(5)	2259	1103
210	15	1	3150	176400	1	(5)	4	1
	135	121	28350	2116800	11	(5)	16	11
	841	840	841	1189	2	(2) (4)	29 41	1 29
	1369	840	1369	39997	2	(2) (4)	37 47	23 37
	1681	1	353010	209739600	1	(1)	41	1
	2209	529	463890	306759600	23	(1)	47	23
	12769	3360	12769	1392047	4	(2) (4)	113 127	97 113
	16129	9409	3387090	5063032800	97	(1)	127	97
	1341015	1142761	281613150	2472936429600	1069	(5)	1576	1069
	3384375	1042441	710718750	18026077860000	1021	(5)	2104	1021
213	7680000	724201	1635840000	65867585284800	851	(5)	2899	851
214	278307	113569	59557698	419617848552	337	(5)	626	337
215	3844	361	826460	748012950	19	(1)	62	19
219	121	25	26499	4220568	5	(1)	11	5
	121	48	8833	762047	4	(4)	13	11
	1849	1728	134977	17644319	24	(2)	43	11
	67081	3072	4896913	10824994873	32	(2)	259	253
	58262689	42398400	58262689	305025663887	440	(2) (4)	7633 10033	3983 7633
	100661089	15864289	22044778491	3232190700929520	3983	(1)	10033	3983
	287133025	286613184	287133025	292642064785	1144	(4)	23953	16945
	392475721	29128368	28650727633	4836198251027737	3116	(4)	20533	19811
221	34225	31824	34225	2329705	12	(2) (4)	185 257	49 185
	66049	2401	14596829	55731488280	49	(1)	257	49
226	81	32	9153	804447	4	(2)	9	7
	1681	1568	189953	29841153	28	(4)	57	41
	3249	113	6498	523488	1	(2)	57	56
	54289	11025	12269314	42080903488	105	(1) (2)	233 233	105 208
	1311025	815409	296291650	3993620181760	903	(3) (2) (1)	903 1145 1145	704 704 903
	57532225	57407616	57532225	28705531105	504	(2) (4)	7585 10721	353 7585
	114939841	124609	25976404066	4186665768761280	353	(1)	10721	353
230	1849	405	85054	24202808	9	(2)	43	38
231	4225	3696	4225	133055	4	(2) (4)	65 89	23 65
	7921	529	1829751	2469547080	23	(1)	89	23
238	1800	1681	428400	100259880	41	(5)	59	41
	3481	119	6962	580560	1	(4)	60	59
239	14400	14161	3441600	1158413880	119	(1) (5) (4)	120 169 169	119 119 120
246	578	529	142188	21604212	23	(3)	23	7
	1107	49	272322	141970536	7	(5)	34	7
247	35976004	34539129	8886072988	234370286171450	5877	(1)	5998	5877
253	125316	91091	2882268	3360488370	91	(2)	354	185
254	147968	25921	37583872	226847546304	161	(5)	417	161
	173889	122047	347778	146090112	31	(4)	544	417
255	16	1	4080	260100	1	(1)	4	1
	66049	16320	66049	16448257	8	(2) (4)	257 287	223 257
	82369	49729	21004095	76738863600	223	(1)	287	223
257	23409	10816	6016113	13086618615	104	(1) (5) (4)	153 185 185	104 104 153
	119617969	5234944	30741818033	5384904750335895	2288	(1) (2)	10937 10937	2288 10695
	192293825	138109504	49419513025	7644364360749345	11752	(3) (5)	11752 18177	7361 11752
	330403329	54184321	84913655553	24408794991856080	7361	(1)	18177	7361
262	107898050	91259809	28269289100	2535777620623260	9553	(3)	9553	4079
	199157859	16638241	52179359058	11877559995005640	4079	(5)	14690	4079
265	49	4	12985	1474725	2	(1)	7	2
	961	484	254665	111025725	22	(1)	31	22
	6625	1296	1755625	2281259125	36	(5)	89	36
	7921	5329	2099065	2250009000	73	(1)	89	73
	362785	304704	96138025	511602397525	552	(3) (5)	552 817	241 552
	667489	58081	176884585	2343606003600	241	(1)	817	241
285	66863329	50274000	66863329	360459159983	420	(2)	8177	4073
	117137329	16589329	33384138765	6038244052659000	4073	(1)	10823	4073
286	13	9	3718	163592	3	(3)	3	2
	15625	10296	15625	1469125	6	(2) (4)	125 161	73 125
	25921	5329	7413406	19753734000	73	(1)	161	73
291	49	48	4753	65863	4	(2)	7	1
	529	432	51313	6708617	12	(4)	31	23
	17161	15625	4993851	4614775776	125	(1)	131	125
	156025	109561	45403275	217819855440	331	(1)	395	331
	22137025	912576	22137025	104066163935	56	(4)	4801	4705
	23049601	21224449	6707433891	214237422347760	4607	(1)	4801	4607
295	1164241	710649	343451095	5041677457700	843	(1)	1079	843
299	36	13	828	22218	1	(4)	7	6
	1872	1849	559728	65441532	43	(5)	61	43
	3025	1369	904475	767060580	37	(1)	55	37
	2146225	2109744	2146225	577258345	84	(4)	2063	1465
	4255969	36481	1272534731	45392960809560	191	(1)	2063	191
	4313088	841	1289613312	46311543210816	29	(5)	2077	29
	5958481	1651225	1781585819	72253492332372	1285	(1)	2441	1285

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

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E-mail : kc2h-msm@asahi-net.or.jp

Hisanori Mishima