Congruum g : 700 <= g <= 799

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 35 congruum g : 700 <= g <= 799.
The solution of the following numbers are found.

719

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

701, 703, 717, 718, 727, 733, 742, 743,
757, 758, 766, 767, 773, 781, 789, 797

Congruum g : 700 <= g <= 799

g	m	n	x	y	z	type	i	j
709	204901	44100	145274809	1709961412123	210	(5)	499	210
710	1440	1369	1022400	320607600	37	(5)	53	37
719	350438400	272613121	251965209600	79473346962216480	16511	(1) (5) (4)	18720 24961 24961	16511 16511 18720
721	112	9	80752	22873004	3	(5)	11	3
	3025	2304	2181025	2087161615	48	(1) (5) (4)	55 73 73	48 48 55
	8464	8343	59248	2429812	9	(2)	92	11
	159390625	50250816	159390625	1909684176625	264	(4)	14479	12625
	345997201	319694400	249463981921	47651516683186031	17880	(5) (4)	25801 25801	17880 18601
723	10609	1200	2556769	4062010897	20	(2)	103	97
	51529	29929	37255467	185108793480	173	(1)	227	173
	9284209	307200	2237494369	105780363172847	320	(4)	3097	3047
731	1521	688	25857	3708159	4	(4)	47	39
	5625	121	4111875	8336031600	11	(1)	75	11
	516961	116272	8788337	25385618679	52	(2)	719	633
734	829472	18769	608832448	15018808345968	137	(5)	921	137
	848241	810703	1696482	650063904	47	(4)	1288	921
741	70225	47424	70225	13725145	8	(2) (4)	265 343	151 265
749	207152	94249	155156848	1721045599812	307	(5)	549	307
751	270400	53361	203070400	2836902469960	231	(1) (5) (4)	520 569 569	231 231 520
759	70225	12144	70225	18329255	4	(2) (4)	265 287	241 265
761	640001	1600	487040761	10748468965491	40	(5)	801	40
	2499561	672400	1902165921	79902649977969	820	(1) (5) (4)	1581 1781 1781	820 820 1581
777	1024	999	7168	133280	3	(2)	32	5
	1681	169	1306137	1485173340	13	(1)	41	13
	53567761	15342889	41622150297	8135785098752220	3917	(1)	7319	3917
782	24200	5041	18924400	80519365080	71	(5)	171	71
	29241	19159	58482	10684080	7	(4)	220	171
790	77440	1521	61177600	478415088800	39	(5)	281	39
791	225	1	177975	75081720	1	(1)	15	1
793	19825	17424	15721225	29735124965	132	(3) (5)	132 193	49 132
	63001	39601	49959793	274643512260	199	(1)	251	199
	724201	368449	574291393	11848232047860	607	(1)	851	607
798	3996001	1442401	3188808798	167930360176320	1201	(1)	1999	1201
799	64	17	3008	159048	1	(4)	9	8
	19228225	16568064	19228225	42790027105	144	(2) (4)	4385 5983	1631 4385

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