11.解と恒等式の一覧表
7/p=1/a+1/b+1/c, final (2〜47)
p | a | b | c |
P | A | B | C |
type |
3 | 1 | 1 | 3 | 7n-4 | 2n-1 | 2n-1 | (2n-1)(7n-4) | A=B or B=C |
5 | 1 | 3 | 15 | 14n-9 | 2n-1 | (8n-5)(2n-1) | (14n-9)(8n-5) | A, AB, BP |
5 | 1 | 5 | 5 | 7n-2 | n | n(7n-2) | n(7n-2) | A=B or B=C |
7 | 2 | 3 | 6 | 1 | 2 | 3 | 6 | 1の分割 |
7 | 2 | 4 | 4 | 1 | 2 | 4 | 4 | 1の分割 |
7 | 3 | 3 | 3 | 1 | 3 | 3 | 3 | 1の分割 |
11 | 2 | 8 | 88 | 28n-17 | 2(2n-1) | 4(5n-3)(2n-1) | 4(28n-17)(5n-3) | A, AB, BP |
11 | 2 | 11 | 22 | 6n-1 | n | 6n-1 | n(6n-1) | B=kP |
13 | 2 | 27 | 702 | 28n-15 | 2(2n-1) | (58n-31)(2n-1) | 2(28n-15)(58n-31) | A, AB, BP |
13 | 2 | 28 | 364 | 28n-15 | 2(2n-1) | 4(15n-8)(2n-1) | 4(28n-15)(15n-8) | A, AB, BP |
13 | 2 | 30 | 195 | 21n-8 | 3n-1 | 3(8n-3)(3n-1) | 3(21n-8)(8n-3) | A, AB, BP |
13 | 2 | 39 | 78 | 20n-7 | 3n-1 | 3(20n-7) | 3(3n-1)(20n-7) | B=kP |
13 | 2 | 52 | 52 | 7n-1 | n | 2n(7n-1) | 2n(7n-1) | A=B or B=C |
13 | 3 | 5 | 195 | 42n-29 | 3(2n-1) | (16n-11)(2n-1) | 3(42n-29)(16n-11) | A, AB, BP |
13 | 3 | 6 | 26 | 28n-15 | 4n-1 | 2(2n-1)(4n-1) | 2(28n-15)(2n-1) | A, AB, BP |
13 | 4 | 4 | 26 | 7n-1 | 2n | 2n | n(7n-1) | A=B or B=C |
17 | 3 | 13 | 663 | 42n-25 | 3(2n-1) | (32n-19)(2n-1) | 3(42n-25)(32n-19) | A, AB, BP |
17 | 3 | 15 | 85 | 14n-11 | 2n-1 | (4n-3)(2n-1) | (14n-11)(4n-3) | A, AB, BP |
17 | 3 | 17 | 51 | 6n-1 | n | 6n-1 | n(6n-1) | B=kP |
17 | 5 | 5 | 85 | 7n-4 | 2n-1 | 2n-1 | (2n-1)(7n-4) | A=B or B=C |
19 | 3 | 29 | 1653 | 42n-23 | 3(2n-1) | (64n-35)(2n-1) | 3(42n-23)(64n-35) | A, AB, BP |
19 | 3 | 30 | 570 | 42n-23 | 3(2n-1) | 6(11n-6)(2n-1) | 6(42n-23)(11n-6) | A, AB, BP |
19 | 3 | 33 | 209 | 14n-9 | 2n-1 | (8n-5)(2n-1) | (14n-9)(8n-5) | A, AB, BP |
19 | 3 | 38 | 114 | 13n-7 | 2n-1 | 2(13n-7) | 2(2n-1)(13n-7) | B=kP |
19 | 3 | 57 | 57 | 7n-2 | n | n(7n-2) | n(7n-2) | A=B or B=C |
19 | 5 | 6 | 570 | 70n-51 | 5(2n-1) | 2(11n-8)(2n-1) | 10(70n-51)(11n-8) | A, AB, BP |
23 | 4 | 20 | 230 | 42n-19 | 2(3n-1) | 2(9n-4)(3n-1) | 2(42n-19)(9n-4) | A, AB, BP |
23 | 4 | 23 | 92 | 6n-1 | n | 6n-1 | n(6n-1) | B=kP |
23 | 5 | 10 | 230 | 70n-47 | 5(2n-1) | 10(3n-2)(2n-1) | 10(70n-47)(3n-2) | A, AB, BP |
29 | 5 | 25 | 725 | 70n-41 | 5(2n-1) | 5(12n-7)(2n-1) | 5(70n-41)(12n-7) | A, AB, BP |
29 | 5 | 29 | 145 | 6n-1 | n | 6n-1 | n(6n-1) | B=kP |
31 | 5 | 39 | 6045 | 70n-39 | 5(2n-1) | (88n-49)(2n-1) | 5(70n-39)(88n-49) | A, AB, BP |
31 | 5 | 40 | 1240 | 70n-39 | 5(2n-1) | 10(9n-5)(2n-1) | 10(70n-39)(9n-5) | A, AB, BP |
31 | 5 | 45 | 279 | 14n-11 | 2n-1 | (4n-3)(2n-1) | (14n-11)(4n-3) | A, AB, BP |
31 | 6 | 17 | 3162 | 84n-53 | 6(2n-1) | (46n-29)(2n-1) | 6(84n-53)(46n-29) | A, AB, BP |
31 | 6 | 18 | 279 | 63n-32 | 3(3n-1) | 9(2n-1)(3n-1) | 9(63n-32)(2n-1) | A, AB, BP |
31 | 8 | 10 | 1240 | 112n-81 | 8(2n-1) | 2(18n-13)(2n-1) | 8(112n-81)(18n-13) | A, AB, BP |
31 | 9 | 9 | 279 | 7n-4 | 2n-1 | 2n-1 | (2n-1)(7n-4) | A=B or B=C |
37 | 6 | 45 | 3330 | 84n-47 | 6(2n-1) | 3(34n-19)(2n-1) | 6(84n-47)(34n-19) | A, AB, BP |
37 | 6 | 48 | 592 | 28n-19 | 2(2n-1) | 4(3n-2)(2n-1) | 4(28n-19)(3n-2) | A, AB, BP |
37 | 6 | 74 | 111 | 13n-2 | 2n | 2(13n-2) | n(13n-2) | B=kP |
37 | 8 | 16 | 592 | 84n-47 | 4(3n-1) | 2(9n-5)(3n-1) | 4(84n-47)(9n-5) | A, AB, BP |
41 | 6 | 247 | 60762 | 84n-43 | 6(2n-1) | (506n-259)(2n-1) | 6(84n-43)(506n-259) | A, AB, BP |
41 | 6 | 248 | 30504 | 84n-43 | 6(2n-1) | 4(127n-65)(2n-1) | 12(84n-43)(127n-65) | A, AB, BP |
41 | 6 | 249 | 20418 | 84n-43 | 6(2n-1) | 3(170n-87)(2n-1) | 6(84n-43)(170n-87) | A, AB, BP |
41 | 6 | 250 | 15375 | 63n-22 | 3(3n-1) | (192n-67)(3n-1) | 3(63n-22)(192n-67) | A, AB, BP |
41 | 6 | 252 | 10332 | 84n-43 | 6(2n-1) | 12(43n-22)(2n-1) | 12(84n-43)(43n-22) | A, AB, BP |
41 | 6 | 255 | 6970 | 28n-15 | 2(2n-1) | (58n-31)(2n-1) | 2(28n-15)(58n-31) | A, AB, BP |
41 | 6 | 258 | 5289 | 63n-22 | 3(3n-1) | 3(66n-23)(3n-1) | 3(63n-22)(66n-23) | A, AB, BP |
41 | 6 | 264 | 3608 | 28n-15 | 2(2n-1) | 4(15n-8)(2n-1) | 4(28n-15)(15n-8) | A, AB, BP |
41 | 6 | 282 | 1927 | 28n-15 | 2(2n-1) | 2(32n-17)(2n-1) | (28n-15)(32n-17) | A, AB, BP |
41 | 6 | 287 | 1722 | 48n-7 | 7n-1 | 7(48n-7) | 7(7n-1)(48n-7) | B=kP |
41 | 6 | 328 | 984 | 55n-14 | 2(4n-1) | 8(55n-14) | 8(4n-1)(55n-14) | B=kP |
41 | 6 | 369 | 738 | 62n-21 | 3(3n-1) | 9(62n-21) | 9(3n-1)(62n-21) | B=kP |
41 | 6 | 410 | 615 | 69n-28 | 2(5n-2) | 10(69n-28) | 5(5n-2)(69n-28) | B=kP |
41 | 6 | 492 | 492 | 7n-1 | n | 2n(7n-1) | 2n(7n-1) | A=B or B=C |
41 | 7 | 36 | 10332 | 98n-57 | 7(2n-1) | 2(43n-25)(2n-1) | 14(98n-57)(43n-25) | A, AB, BP |
41 | 7 | 41 | 287 | 6n-1 | n | 6n-1 | n(6n-1) | B=kP |
41 | 7 | 42 | 246 | 28n-15 | 4n-1 | 2(2n-1)(4n-1) | 2(28n-15)(2n-1) | A, AB, BP |
41 | 8 | 22 | 3608 | 112n-71 | 8(2n-1) | 2(30n-19)(2n-1) | 8(112n-71)(30n-19) | A, AB, BP |
41 | 8 | 24 | 246 | 70n-29 | 2(5n-1) | 2(5n-2)(5n-1) | 2(70n-29)(5n-2) | A, AB, BP |
41 | 9 | 18 | 246 | 84n-43 | 3(4n-1) | 6(2n-1)(4n-1) | 6(84n-43)(2n-1) | A, AB, BP |
41 | 10 | 15 | 246 | 84n-43 | 2(6n-1) | 3(2n-1)(6n-1) | 6(84n-43)(2n-1) | A, AB, BP |
41 | 12 | 12 | 246 | 7n-1 | 2n | 2n | n(7n-1) | A=B or B=C |
43 | 10 | 16 | 3440 | 140n-97 | 10(2n-1) | 4(13n-9)(2n-1) | 20(140n-97)(13n-9) | A, AB, BP |
47 | 7 | 165 | 54285 | 98n-51 | 7(2n-1) | (344n-179)(2n-1) | 7(98n-51)(344n-179) | A, AB, BP |
47 | 7 | 168 | 7896 | 98n-51 | 7(2n-1) | 14(25n-13)(2n-1) | 14(98n-51)(25n-13) | A, AB, BP |
47 | 7 | 188 | 1316 | 27n-7 | 4n-1 | 4(27n-7) | 4(4n-1)(27n-7) | B=kP |
47 | 7 | 189 | 1269 | 14n-9 | 2n-1 | (8n-5)(2n-1) | (14n-9)(8n-5) | A, AB, BP |
47 | 7 | 329 | 329 | 7n-2 | n | n(7n-2) | n(7n-2) | A=B or B=C |
47 | 8 | 42 | 7896 | 112n-65 | 8(2n-1) | 2(50n-29)(2n-1) | 8(112n-65)(50n-29) | A, AB, BP |
47 | 8 | 47 | 376 | 6n-1 | n | 6n-1 | n(6n-1) | B=kP |
47 | 9 | 27 | 1269 | 42n-37 | 3(2n-1) | (8n-7)(2n-1) | 3(42n-37)(8n-7) | A, AB, BP |
E-mail : kc2h-msm@asahi-net.or.jp三島 久典