With 2 triples, inifinite solutions, smallest :
∑=19 for (2,8,9), (3,4,12)
∏=90 for (1,9,10), (2,3,15)
With 3 triples, inifinite solutions, smallest :
∑=39 for (4,15,20), (5,10,24), (6,8,25)
∏=1200 for (4,15,20), (5,10,24), (6,8,25)
With 4 triples, inifinite solutions, smallest :
∑=118 for (14,50,54), (15,40,63), (18,30,70), (21,25,72)J.G. Mauldon
∏=25200 for (6,56,75), (7,40,90), (9,28,100), (12,20,105)J.G. Mauldon
With 5 triples, single solution :
∑=981 for (6,480,495), (11,160,810), (12,144,825), (20,81,880), (33,48,900)J.G. Mauldon
∏=1425600 for (6,480,495), (11,160,810), (12,144,825), (20,81,880), (33,48,900)J.G. Mauldon
Contributions
With 5 triples, several solutions found:
| triples | ∑ | ∏ | amin | amax |
|---|
| (11,84,90) (12,63,110) (15,44,126) (18,35,132) (22,28,135) | 185 | 83160 | 11 | 135 |
| (8,168,270) (10,112,324) (14,72,360) (20,48,378) (27,35,384) | 446 | 362880 | 8 | 384 |
| (6,253,504) (8,161,594) (9,138,616) (11,108,644) (24,46,693) | 763 | 765072 | 6 | 693 |
| (8,132,315) (9,110,336) (11,84,360) (16,54,385) (24,35,396) | 455 | 332640 | 8 | 396 |
| (5,792,855) (9,275,1368) (11,216,1425) (15,152,1485) (25,88,1539) | 1652 | 3385800 | 5 | 1539 |
| (5,396,1680) (6,315,1760) (8,225,1848) (12,144,1925) (21,80,1980) | 2081 | 3326400 | 5 | 1980 |
| (4,1666,2430) (5,1071,3024) (14,306,3780) (27,153,3920) (51,80,3969) | 4100 | 16193520 | 4 | 3969 |
| (4,1188,3451) (6,693,3944) (11,348,4284) (24,153,4466) (29,126,4488) | 4643 | 16399152 | 4 | 4488 |
| (3,3472,4554) (4,1953,6072) (22,279,7728) (33,184,7812) (42,144,7843) | 8029 | 47434464 | 3 | 7843 |
| ... |
| view more ▼ |
With 6 triples, several solutions found:
| triples | ∑ | ∏ | amin | amax |
|---|
| (14,231,240) (15,176,294) (16,154,315) (28,72,385) (33,60,392) (40,49,396) | 485 | 776160 | 14 | 392 |
| (12,728,765) (13,540,952) (21,260,1224) (24,221,1260) (35,144,1326) (54,91,1360) | 1505 | 6683040 | 12 | 1260 |
| (11,1024,1155) (12,770,1408) (16,480,1694) (22,320,1848) (28,242,1920) (30,224,1936) | 2190 | 13009920 | 11 | 1920 |
| ... |
| view more ▼ |
With 7 triples, single solution found:
| triples | ∑ | ∏ | amin | amax |
|---|
| (12,728,765) (13,540,952) (21,260,1224) (24,221,1260) (35,144,1326) (54,91,1360) (68,72,1365) | 1505 | 6683040 | 14 | 392 |
With 8 triples : no solution found with (a,b,c) < 10000.