Section 10. Congruum

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
There are 37 congruum g : 200 <= g <= 299.
The solution of the following numbers are not in the range of 1 <= m, n <= 1,000,000.

206, 213, 223, 229, 237, 247, 262,
263, 269, 271, 277, 278, 287, 293

Congruum g : 200 <= g <= 299
g m n x y z

205 45 4 9225 882525 2

210 5 2 525 11025 1

6 1 1260 44100 1

8 7 240 1800 1

128 7 3840 237600 1

486 361 102060 21829500 19

605 578 63525 4729725 17

841 840 841 1189 2

1369 840 1369 39997 2

12769 3360 12769 1392047 4

71286 48841 14970060 42190161300 221

120125 3698 12613125 44774233875 43

214 195938 82369 41930732 246361001676 287

215 3844 361 826460 748012950 19

219 73 48 5329 293095 4

121 48 8833 762047 4

1849 1728 134977 17644319 24

67081 3072 4896913 10824994873 32

221 13 4 2873 146523 2

34225 31824 34225 2329705 12

222 12506 3481 2776332 4443199020 59

226 81 32 9153 804447 4

1681 1568 189953 29841153 28

32657 21632 3690241 5310690945 104

230 1127 722 129605 35826525 19

231 7 4 1617 53361 2

4225 3696 4225 133055 4

238 1800 1681 428400 100259880 41

239 14400 14161 3441600 1158413880 119

246 578 529 142188 21604212 23

253 125316 91091 2882268 3360488370 91

254 147968 25921 37583872 226847546304 161

255 16 1 4080 260100 1

66049 16320 66049 16448257 8

257 23409 10816 6016113 13086618615 104

265 49 4 12985 1474725 2

961 484 254665 111025725 22

6625 1296 1755625 2281259125 36

362785 304704 96138025 511602397525 552

285 76 49 21660 2436750 7

286 11 2 1573 61347 1

15625 10296 15625 1469125 6

291 49 48 4753 65863 4

529 432 51313 6708617 12

16393 768 1590121 2002940875 16

132793 23232 12880921 45516649085 88

295 937445 226796 4687225 9846387525 62

299 36 13 828 22218 1

1872 1849 559728 65441532 43

2197 828 28561 4470895 6

**Congruum g : 200 <= g <= 299**
g	m	n	x	y	z
205	45	4	9225	882525	2
210	5	2	525	11025	1
6	1	1260	44100	1
8	7	240	1800	1
128	7	3840	237600	1
486	361	102060	21829500	19
605	578	63525	4729725	17
841	840	841	1189	2
1369	840	1369	39997	2
12769	3360	12769	1392047	4
71286	48841	14970060	42190161300	221
120125	3698	12613125	44774233875	43
214	195938	82369	41930732	246361001676	287
215	3844	361	826460	748012950	19
219	73	48	5329	293095	4
121	48	8833	762047	4
1849	1728	134977	17644319	24
67081	3072	4896913	10824994873	32
221	13	4	2873	146523	2
34225	31824	34225	2329705	12
222	12506	3481	2776332	4443199020	59
226	81	32	9153	804447	4
1681	1568	189953	29841153	28
32657	21632	3690241	5310690945	104
230	1127	722	129605	35826525	19
231	7	4	1617	53361	2
4225	3696	4225	133055	4
238	1800	1681	428400	100259880	41
239	14400	14161	3441600	1158413880	119
246	578	529	142188	21604212	23
253	125316	91091	2882268	3360488370	91
254	147968	25921	37583872	226847546304	161
255	16	1	4080	260100	1
66049	16320	66049	16448257	8
257	23409	10816	6016113	13086618615	104
265	49	4	12985	1474725	2
961	484	254665	111025725	22
6625	1296	1755625	2281259125	36
362785	304704	96138025	511602397525	552
285	76	49	21660	2436750	7
286	11	2	1573	61347	1
15625	10296	15625	1469125	6
291	49	48	4753	65863	4
529	432	51313	6708617	12
16393	768	1590121	2002940875	16
132793	23232	12880921	45516649085	88
295	937445	226796	4687225	9846387525	62
299	36	13	828	22218	1
1872	1849	559728	65441532	43
2197	828	28561	4470895	6

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

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

Hisanori Mishima