I minimi interi esprimibili come somma di tre biquadrati in esattamente n modi differenti, per n da 1 a 21

La tabella seguente mostra i minimi interi esprimibili come somma di tre biquadrati in esattamente n modi differenti, per n da 1 a 21 (Duncan Moore).

n

Numero

Rappresentazioni

1

3

14 + 14 + 14

2

2673

74 + 44 + 24 = 64 + 64 + 34

3

811538

294 + 174 + 124 = 284 + 214 + 74 = 274 + 234 + 44

4

5978882

484 + 254 + 234 = 474 + 324 + 154 = 454 + 374 + 84 = 434 + 404 + 34

5

137149922

1054 + 564 + 494 = 1044 + 654 + 394 = 994 + 804 + 194 = 964 + 854 + 114 = 914 + 914 + 04

6

292965218

1274 + 664 + 614 = 1264 + 774 + 494 = 1234 + 894 + 344 = 1214 + 944 + 274 = 1194 + 984 + 214 = 1114 + 1094 + 24

7

779888018

1674 + 384 + 94 = 1624 + 894 + 734 = 1614 + 984 + 634 = 1584 + 1114 + 474 = 1574 + 1144 + 434 = 1474 + 1334 + 144 = 1424 + 1394 + 34

8

5745705602

2674 + 1454 + 1224 = 2654 + 1634 + 1024 = 2634 + 1734 + 904 = 2624 + 1774 + 854 = 2554 + 1974 + 584 = 2504 + 2074 + 434 = 2434 + 2184 + 254 = 2334 + 2304 + 34

9

105760443698

5534 + 3014 + 2524 = 5514 + 3234 + 2284 = 5494 + 3374 + 2124 = 5474 + 3484 + 1994 = 5324 + 3994 + 1334 = 5244 + 4174 + 1074 = 5134 + 4374 + 764 = 5034 + 4524 + 514 = 4834 + 4764 + 74

10

49511121842

4584 + 2334 + 2254 = 4574 + 2554 + 2024 = 4554 + 2734 + 1824 = 4474 + 3104 + 1374 = 4424 + 3254 + 1174 = 4414 + 3224 + 1754 = 4384 + 3354 + 1034 = 4274 + 3574 + 704 = 4134 + 3784 + 354 = 4034 + 3904 + 134

11

1872511131218

11694 + 2664 + 634 = 11344 + 6234 + 5114 = 11274 + 6864 + 4414 = 11234 + 7094 + 4144 = 11214 + 7194 + 4024 = 11064 + 7774 + 3294 = 10994 + 7984 + 3014 = 10774 + 8514 + 2264 = 10414 + 9144 + 1274 = 10294 + 9314 + 984 = 9944 + 9734 + 214

12

281539574498

7074 + 3714 + 3364 = 7044 + 4114 + 2934 = 7014 + 4324 + 2694 = 6994 + 4434 + 2564 = 6964 + 4574 + 2394 = 6934 + 4694 + 2244 = 6794 + 5114 + 1684 = 6644 + 5434 + 1214 = 6564 + 5574 + 994 = 6494 + 5684 + 814 = 6324 + 5914 + 414 = 6164 + 6094 + 74

13

17673688436978

19874 + 11014 + 8864 = 19814 + 11624 + 8194 = 19744 + 12114 + 7634 = 19634 + 12694 + 6944 = 19464 + 13374 + 6094 = 19414 + 13544 + 5874 = 19294 + 13914 + 5384 = 19134 + 14344 + 4794 = 17994 + 16384 + 1614 = 17894 + 16514 + 1384 = 17664 + 16794 + 874 = 17374 + 17114 + 264 = 16944 + 15894 + 13234

14

17873514984962

19954 + 10644 + 9314 = 19894 + 11444 + 8454 = 19844 + 11854 + 7994 = 19764 + 12354 + 7414 = 19614 + 13054 + 6564 = 19604 + 13094 + 6514 = 19254 + 14214 + 5044 = 19114 + 14564 + 4554 = 18814 + 15204 + 3614 = 18594 + 15604 + 2994 = 18404 + 15914 + 2494 = 18244 + 16154 + 2094 = 17754 + 16794 + 964 = 17294 + 17294 + 04

15

253930825318898

38764 + 19574 + 19194 = 38714 + 21074 + 17644 = 38574 + 22614 + 15964 = 38434 + 23594 + 14844 = 38294 + 24364 + 13934 = 37794 + 26364 + 11434 = 37694 + 26684 + 11014 = 37564 + 27074 + 10494 = 37244 + 27934 + 9314 = 36684 + 29194 + 7494 = 36574 + 29414 + 7164 = 35914 + 30594 + 5324 = 35214 + 31644 + 3574 = 34394 + 32684 + 1714 = 33814 + 33324 + 494

16

7865870969138

16264 + 8294 + 7974 = 16224 + 9114 + 7114 = 16214 + 9224 + 6994 = 16194 + 9414 + 6784 = 16114 + 9974 + 6144 = 16014 + 10474 + 5544 = 15794 + 11264 + 4534 = 15784 + 11294 + 4494 = 15714 + 11494 + 4224 = 15534 + 11944 + 3594 = 15494 + 12034 + 3464 = 15034 + 12894 + 2144 = 14944 + 13034 + 1914 = 14814 + 13224 + 1594 = 14474 + 13664 + 814 = 14344 + 13814 + 534

17

768054952462322

51104 + 26674 + 24434 = 51074 + 27424 + 23654 = 51054 + 27784 + 23274 = 50824 + 30174 + 20654 = 50334 + 32904 + 17434 = 50304 + 33034 + 17274 = 50054 + 34024 + 16034 = 49384 + 36134 + 13254 = 49234 + 36534 + 12704 = 48374 + 38504 + 9874 = 48234 + 38784 + 9454 = 47934 + 39354 + 8584 = 46974 + 40954 + 6024 = 45754 + 42624 + 3134 = 45154 + 43334 + 1824 = 45074 + 43424 + 1654 = 43824 + 38854 + 36194

18

47580188090162

25484 + 13654 + 11834 = 25454 + 14134 + 11324 = 25404 + 14674 + 10734 = 25354 + 15084 + 10274 = 25254 + 15724 + 9534 = 25234 + 15834 + 9404 = 25154 + 16234 + 8924 = 24924 + 17154 + 7774 = 24874 + 17324 + 7554 = 24574 + 18204 + 6374 = 24434 + 18554 + 5884 = 24054 + 19374 + 4684 = 23724 + 19974 + 3754 = 23534 + 20284 + 3254 = 23274 + 20674 + 2604 = 23034 + 21004 + 2034 = 22934 + 21134 + 1804 = 22124 + 22054 + 74

19

101635786393778

31734 + 7224 + 1714 = 30834 + 15424 + 15414 = 30824 + 16094 + 14734 = 30784 + 16914 + 13874 = 30664 + 18134 + 12534 = 30594 + 18624 + 11974 = 30374 + 19784 + 10594 = 30174 + 20584 + 9594 = 30024 + 21094 + 8934 = 29834 + 21664 + 8174 = 29674 + 22094 + 7584 = 29574 + 22344 + 7234 = 29344 + 22874 + 6474 = 28914 + 23734 + 5184 = 28634 + 24224 + 4414 = 27934 + 25274 + 2664 = 27634 + 25664 + 1974 = 27274 + 26094 + 1184 = 26984 + 26414 + 574

20

675976518369698

49514 + 24884 + 24634 = 49494 + 25974 + 23524 = 49334 + 28324 + 21014 = 49284 + 28774 + 20514 = 49074 + 30244 + 18834 = 48934 + 31014 + 17924 = 48724 + 31994 + 16734 = 48514 + 32834 + 15684 = 48244 + 33774 + 14474 = 48014 + 34484 + 13534 = 47874 + 34884 + 12994 = 47534 + 35774 + 11764 = 47074 + 36834 + 10244 = 46484 + 38014 + 8474 = 45924 + 38994 + 6934 = 45434 + 39764 + 5674 = 44244 + 41374 + 2874 = 43994 + 41674 + 2324 = 43734 + 41974 + 1764 = 43124 + 42634 + 494

21

42434525937184178

139094 + 77074 + 62024 = 138984 + 78414 + 60574 = 138674 + 81344 + 57334 = 138184 + 84774 + 53414 = 137674 + 87584 + 50094 = 137664 + 87634 + 50034 = 137414 + 88834 + 48584 = 136934 + 90914 + 46024 = 136224 + 93594 + 42634 = 135874 + 94784 + 41094 = 135034 + 97374 + 37664 = 133914 + 100384 + 33534 = 132384 + 103914 + 28474 = 129094 + 110024 + 19074 = 127424 + 112594 + 14834 = 125934 + 114664 + 11274 = 125234 + 115574 + 9664 = 123624 + 117534 + 6094 = 122344 + 118974 + 3374 = 121594 + 119774 + 1824 = 118584 + 111234 + 92614