11．解と恒等式の一覧表
6/p＝1/a＋1/b＋1/c, final (2〜47)
| p | a | b | c |
P | A | B | C |
type |
|---|
| 2 | 1 | 1 | 1 | 2 | 1 | 1 | 1 | ２の分割 |
|---|
| 3 | 1 | 2 | 2 | 1 | 1 | 2 | 2 | １の分割 |
|---|
| 5 | 1 | 6 | 30 | 12n-7 | 2n-1 | 2(7n-4)(2n-1) | 2(12n-7)(7n-4) | A, AB, BP |
|---|
| 5 | 1 | 10 | 10 | 6n-1 | n | 2n(6n-1) | 2n(6n-1) | A=B or B=C |
|---|
| 5 | 2 | 2 | 5 | 6n-1 | 2n | 2n | n(6n-1) | A=B or B=C |
|---|
| 7 | 2 | 3 | 42 | 24n-17 | 2(2n-1) | (10n-7)(2n-1) | 2(24n-17)(10n-7) | A, AB, BP |
|---|
| 11 | 2 | 23 | 506 | 24n-13 | 2(2n-1) | (50n-27)(2n-1) | 2(24n-13)(50n-27) | A, AB, BP |
|---|
| 11 | 2 | 24 | 264 | 24n-13 | 2(2n-1) | 4(13n-7)(2n-1) | 4(24n-13)(13n-7) | A, AB, BP |
|---|
| 11 | 2 | 26 | 143 | 18n-7 | 3n-1 | (21n-8)(3n-1) | (18n-7)(21n-8) | A, AB, BP |
|---|
| 11 | 2 | 33 | 66 | 17n-6 | 3n-1 | 3(17n-6) | 3(3n-1)(17n-6) | B=kP |
|---|
| 11 | 2 | 44 | 44 | 6n-1 | n | 2n(6n-1) | 2n(6n-1) | A=B or B=C |
|---|
| 11 | 3 | 6 | 22 | 24n-13 | 4n-1 | 2(2n-1)(4n-1) | 2(24n-13)(2n-1) | A, AB, BP |
|---|
| 11 | 4 | 4 | 22 | 6n-1 | 2n | 2n | n(6n-1) | A=B or B=C |
|---|
| 13 | 3 | 8 | 312 | 36n-23 | 3(2n-1) | 2(11n-7)(2n-1) | 6(36n-23)(11n-7) | A, AB, BP |
|---|
| 17 | 3 | 52 | 2652 | 36n-19 | 3(2n-1) | 2(55n-29)(2n-1) | 6(36n-19)(55n-29) | A, AB, BP |
|---|
| 17 | 3 | 54 | 918 | 36n-19 | 3(2n-1) | 6(19n-10)(2n-1) | 6(36n-19)(19n-10) | A, AB, BP |
|---|
| 17 | 3 | 60 | 340 | 12n-7 | 2n-1 | 2(7n-4)(2n-1) | 2(12n-7)(7n-4) | A, AB, BP |
|---|
| 17 | 3 | 68 | 204 | 23n-6 | 4n-1 | 4(23n-6) | 4(4n-1)(23n-6) | B=kP |
|---|
| 17 | 3 | 102 | 102 | 6n-1 | n | 2n(6n-1) | 2n(6n-1) | A=B or B=C |
|---|
| 17 | 4 | 10 | 340 | 48n-31 | 4(2n-1) | 2(14n-9)(2n-1) | 4(48n-31)(14n-9) | A, AB, BP |
|---|
| 17 | 4 | 12 | 51 | 30n-13 | 5n-1 | (5n-2)(5n-1) | (30n-13)(5n-2) | A, AB, BP |
|---|
| 17 | 6 | 6 | 51 | 6n-1 | 2n | 2n | n(6n-1) | A=B or B=C |
|---|
| 19 | 4 | 16 | 304 | 36n-17 | 2(3n-1) | (15n-7)(3n-1) | 2(36n-17)(15n-7) | A, AB, BP |
|---|
| 19 | 4 | 19 | 76 | 5n-1 | n | 5n-1 | n(5n-1) | B=kP |
|---|
| 23 | 4 | 93 | 8556 | 48n-25 | 4(2n-1) | (194n-101)(2n-1) | 4(48n-25)(194n-101) | A, AB, BP |
|---|
| 23 | 4 | 94 | 4324 | 48n-25 | 4(2n-1) | 2(98n-51)(2n-1) | 4(48n-25)(98n-51) | A, AB, BP |
|---|
| 23 | 4 | 96 | 2208 | 36n-13 | 2(3n-1) | 3(25n-9)(3n-1) | 6(36n-13)(25n-9) | A, AB, BP |
|---|
| 23 | 4 | 100 | 1150 | 36n-13 | 2(3n-1) | 2(39n-14)(3n-1) | 2(36n-13)(39n-14) | A, AB, BP |
|---|
| 23 | 4 | 108 | 621 | 18n-13 | 3n-2 | 3(7n-5)(3n-2) | 3(18n-13)(7n-5) | A, AB, BP |
|---|
| 23 | 4 | 115 | 460 | 29n-6 | 5n-1 | 5(29n-6) | 5(5n-1)(29n-6) | B=kP |
|---|
| 23 | 4 | 138 | 276 | 35n-12 | 2(3n-1) | 6(35n-12) | 6(3n-1)(35n-12) | B=kP |
|---|
| 23 | 4 | 184 | 184 | 6n-1 | n | 2n(6n-1) | 2n(6n-1) | A=B or B=C |
|---|
| 23 | 5 | 20 | 92 | 18n-13 | 3n-1 | (3n-2)(3n-1) | (18n-13)(3n-2) | A, AB, BP |
|---|
| 23 | 6 | 12 | 92 | 48n-25 | 2(4n-1) | 4(2n-1)(4n-1) | 4(48n-25)(2n-1) | A, AB, BP |
|---|
| 23 | 8 | 8 | 92 | 6n-1 | 2n | 2n | n(6n-1) | A=B or B=C |
|---|
| 29 | 5 | 146 | 21170 | 60n-31 | 5(2n-1) | 2(151n-78)(2n-1) | 10(60n-31)(151n-78) | A, AB, BP |
|---|
| 29 | 5 | 150 | 4350 | 60n-31 | 5(2n-1) | 10(31n-16)(2n-1) | 10(60n-31)(31n-16) | A, AB, BP |
|---|
| 29 | 5 | 170 | 986 | 12n-7 | 2n-1 | 2(7n-4)(2n-1) | 2(12n-7)(7n-4) | A, AB, BP |
|---|
| 29 | 5 | 174 | 870 | 35n-6 | 6n-1 | 6(35n-6) | 6(6n-1)(35n-6) | B=kP |
|---|
| 29 | 5 | 290 | 290 | 6n-1 | n | 2n(6n-1) | 2n(6n-1) | A=B or B=C |
|---|
| 29 | 6 | 25 | 4350 | 72n-43 | 6(2n-1) | (62n-37)(2n-1) | 6(72n-43)(62n-37) | A, AB, BP |
|---|
| 29 | 6 | 29 | 174 | 5n-1 | n | 5n-1 | n(5n-1) | B=kP |
|---|
| 29 | 6 | 30 | 145 | 24n-19 | 2(2n-1) | 2(4n-3)(2n-1) | (24n-19)(4n-3) | A, AB, BP |
|---|
| 29 | 10 | 10 | 145 | 6n-1 | 2n | 2n | n(6n-1) | A=B or B=C |
|---|
| 31 | 6 | 38 | 1767 | 54n-23 | 3(3n-1) | (33n-14)(3n-1) | 3(54n-23)(33n-14) | A, AB, BP |
|---|
| 31 | 6 | 39 | 806 | 24n-17 | 2(2n-1) | (10n-7)(2n-1) | 2(24n-17)(10n-7) | A, AB, BP |
|---|
| 31 | 6 | 62 | 93 | 11n-2 | 2n | 2(11n-2) | n(11n-2) | B=kP |
|---|
| 37 | 7 | 52 | 13468 | 84n-47 | 7(2n-1) | 2(59n-33)(2n-1) | 14(84n-47)(59n-33) | A, AB, BP |
|---|
| 37 | 8 | 27 | 7992 | 96n-59 | 8(2n-1) | (70n-43)(2n-1) | 8(96n-59)(70n-43) | A, AB, BP |
|---|
| 41 | 7 | 288 | 82656 | 84n-43 | 7(2n-1) | 2(295n-151)(2n-1) | 14(84n-43)(295n-151) | A, AB, BP |
|---|
| 41 | 7 | 294 | 12054 | 84n-43 | 7(2n-1) | 14(43n-22)(2n-1) | 14(84n-43)(43n-22) | A, AB, BP |
|---|
| 41 | 7 | 328 | 2296 | 47n-6 | 8n-1 | 8(47n-6) | 8(8n-1)(47n-6) | B=kP |
|---|
| 41 | 7 | 336 | 1968 | 12n-7 | 2n-1 | 2(7n-4)(2n-1) | 2(12n-7)(7n-4) | A, AB, BP |
|---|
| 41 | 7 | 574 | 574 | 6n-1 | n | 2n(6n-1) | 2n(6n-1) | A=B or B=C |
|---|
| 41 | 8 | 47 | 15416 | 96n-55 | 8(2n-1) | (110n-63)(2n-1) | 8(96n-55)(110n-63) | A, AB, BP |
|---|
| 41 | 8 | 48 | 1968 | 72n-31 | 4(3n-1) | 6(7n-3)(3n-1) | 12(72n-31)(7n-3) | A, AB, BP |
|---|
| 41 | 8 | 56 | 287 | 18n-13 | 3n-1 | (3n-2)(3n-1) | (18n-13)(3n-2) | A, AB, BP |
|---|
| 41 | 12 | 16 | 1968 | 108n-67 | 6(3n-1) | (21n-13)(3n-1) | 6(108n-67)(21n-13) | A, AB, BP |
|---|
| 41 | 14 | 14 | 287 | 6n-1 | 2n | 2n | n(6n-1) | A=B or B=C |
|---|
| 43 | 8 | 69 | 23736 | 96n-53 | 8(2n-1) | (154n-85)(2n-1) | 8(96n-53)(154n-85) | A, AB, BP |
|---|
| 43 | 8 | 72 | 1548 | 36n-29 | 2(3n-2) | 3(5n-4)(3n-2) | 6(36n-29)(5n-4) | A, AB, BP |
|---|
| 43 | 8 | 86 | 344 | 11n-1 | 2n | 2(11n-1) | 2n(11n-1) | B=kP |
|---|
| 43 | 9 | 36 | 1548 | 36n-29 | 3(2n-1) | 2(5n-4)(2n-1) | 6(36n-29)(5n-4) | A, AB, BP |
|---|
| 43 | 12 | 18 | 1548 | 144n-101 | 12(2n-1) | 6(10n-7)(2n-1) | 12(144n-101)(10n-7) | A, AB, BP |
|---|
| 43 | 13 | 16 | 8944 | 156n-113 | 13(2n-1) | 2(29n-21)(2n-1) | 26(156n-113)(29n-21) | A, AB, BP |
|---|
| 47 | 8 | 377 | 141752 | 96n-49 | 8(2n-1) | (770n-393)(2n-1) | 8(96n-49)(770n-393) | A, AB, BP |
|---|
| 47 | 8 | 378 | 71064 | 96n-49 | 8(2n-1) | 2(386n-197)(2n-1) | 8(96n-49)(386n-197) | A, AB, BP |
|---|
| 47 | 8 | 380 | 35720 | 72n-25 | 4(3n-1) | (291n-101)(3n-1) | 4(72n-25)(291n-101) | A, AB, BP |
|---|
| 47 | 8 | 384 | 18048 | 72n-25 | 4(3n-1) | 6(49n-17)(3n-1) | 12(72n-25)(49n-17) | A, AB, BP |
|---|
| 47 | 8 | 392 | 9212 | 36n-25 | 2(3n-2) | (75n-52)(3n-2) | 2(36n-25)(75n-52) | A, AB, BP |
|---|
| 47 | 8 | 408 | 4794 | 36n-25 | 2(3n-2) | 6(13n-9)(3n-2) | 6(36n-25)(13n-9) | A, AB, BP |
|---|
| 47 | 8 | 423 | 3384 | 53n-6 | 9n-1 | 9(53n-6) | 9(9n-1)(53n-6) | B=kP |
|---|
| 47 | 8 | 440 | 2585 | 18n-7 | 3n-1 | (21n-8)(3n-1) | (18n-7)(21n-8) | A, AB, BP |
|---|
| 47 | 8 | 470 | 1880 | 59n-12 | 2(5n-1) | 10(59n-12) | 10(5n-1)(59n-12) | B=kP |
|---|
| 47 | 8 | 564 | 1128 | 71n-24 | 4(3n-1) | 12(71n-24) | 12(3n-1)(71n-24) | B=kP |
|---|
| 47 | 8 | 752 | 752 | 6n-1 | n | 2n(6n-1) | 2n(6n-1) | A=B or B=C |
|---|
| 47 | 9 | 72 | 376 | 30n-13 | 5n-1 | (5n-2)(5n-1) | (30n-13)(5n-2) | A, AB, BP |
|---|
| 47 | 10 | 40 | 376 | 36n-25 | 2(3n-1) | 2(3n-2)(3n-1) | 2(36n-25)(3n-2) | A, AB, BP |
|---|
| 47 | 12 | 24 | 376 | 84n-37 | 2(7n-1) | (7n-3)(7n-1) | 2(84n-37)(7n-3) | A, AB, BP |
|---|
| 47 | 16 | 16 | 376 | 6n-1 | 2n | 2n | n(6n-1) | A=B or B=C |
|---|
E-mail : kc2h-msm@asahi-net.or.jp三島 久典