11.解と恒等式の一覧表
6/p=1/a+1/b+1/c, final (53〜97)
p | a | b | c |
P | A | B | C |
type |
53 | 9 | 478 | 228006 | 108n-55 | 9(2n-1) | 2(487n-248)(2n-1) | 18(108n-55)(487n-248) | A, AB, BP |
53 | 9 | 480 | 76320 | 108n-55 | 9(2n-1) | 6(163n-83)(2n-1) | 18(108n-55)(163n-83) | A, AB, BP |
53 | 9 | 486 | 25758 | 36n-19 | 3(2n-1) | 2(55n-29)(2n-1) | 6(36n-19)(55n-29) | A, AB, BP |
53 | 9 | 504 | 8904 | 36n-19 | 3(2n-1) | 6(19n-10)(2n-1) | 6(36n-19)(19n-10) | A, AB, BP |
53 | 9 | 530 | 4770 | 59n-6 | 10n-1 | 10(59n-6) | 10(10n-1)(59n-6) | B=kP |
53 | 9 | 558 | 3286 | 12n-7 | 2n-1 | 2(7n-4)(2n-1) | 2(12n-7)(7n-4) | A, AB, BP |
53 | 9 | 636 | 1908 | 71n-18 | 3(4n-1) | 12(71n-18) | 12(4n-1)(71n-18) | B=kP |
53 | 9 | 954 | 954 | 6n-1 | n | 2n(6n-1) | 2n(6n-1) | A=B or B=C |
53 | 10 | 76 | 20140 | 120n-67 | 10(2n-1) | 4(43n-24)(2n-1) | 20(120n-67)(43n-24) | A, AB, BP |
53 | 10 | 90 | 477 | 24n-19 | 2(2n-1) | 2(4n-3)(2n-1) | (24n-19)(4n-3) | A, AB, BP |
53 | 10 | 106 | 265 | 11n-2 | 2n | 2(11n-2) | n(11n-2) | B=kP |
53 | 12 | 36 | 477 | 90n-37 | 3(5n-1) | 3(5n-2)(5n-1) | 3(90n-37)(5n-2) | A, AB, BP |
53 | 14 | 24 | 8904 | 168n-115 | 14(2n-1) | 4(19n-13)(2n-1) | 28(168n-115)(19n-13) | A, AB, BP |
53 | 18 | 18 | 477 | 6n-1 | 2n | 2n | n(6n-1) | A=B or B=C |
59 | 10 | 591 | 348690 | 120n-61 | 10(2n-1) | (1202n-611)(2n-1) | 10(120n-61)(1202n-611) | A, AB, BP |
59 | 10 | 592 | 174640 | 120n-61 | 10(2n-1) | 4(301n-153)(2n-1) | 20(120n-61)(301n-153) | A, AB, BP |
59 | 10 | 594 | 87615 | 90n-31 | 5(3n-1) | 3(151n-52)(3n-1) | 15(90n-31)(151n-52) | A, AB, BP |
59 | 10 | 595 | 70210 | 120n-61 | 10(2n-1) | 5(242n-123)(2n-1) | 10(120n-61)(242n-123) | A, AB, BP |
59 | 10 | 600 | 35400 | 120n-61 | 10(2n-1) | 20(61n-31)(2n-1) | 20(120n-61)(61n-31) | A, AB, BP |
59 | 10 | 610 | 17995 | 90n-31 | 5(3n-1) | 5(93n-32)(3n-1) | 5(90n-31)(93n-32) | A, AB, BP |
59 | 10 | 615 | 14514 | 24n-13 | 2(2n-1) | (50n-27)(2n-1) | 2(24n-13)(50n-27) | A, AB, BP |
59 | 10 | 640 | 7552 | 24n-13 | 2(2n-1) | 4(13n-7)(2n-1) | 4(24n-13)(13n-7) | A, AB, BP |
59 | 10 | 649 | 6490 | 65n-6 | 11n-1 | 11(65n-6) | 11(11n-1)(65n-6) | B=kP |
59 | 10 | 690 | 4071 | 18n-13 | 3n-2 | 3(7n-5)(3n-2) | 3(18n-13)(7n-5) | A, AB, BP |
59 | 10 | 708 | 3540 | 71n-12 | 2(6n-1) | 12(71n-12) | 12(6n-1)(71n-12) | B=kP |
59 | 10 | 826 | 2065 | 83n-24 | 2(7n-2) | 14(83n-24) | 7(7n-2)(83n-24) | B=kP |
59 | 10 | 885 | 1770 | 89n-30 | 5(3n-1) | 15(89n-30) | 15(3n-1)(89n-30) | B=kP |
59 | 10 | 1180 | 1180 | 6n-1 | n | 2n(6n-1) | 2n(6n-1) | A=B or B=C |
59 | 11 | 110 | 590 | 18n-13 | 3n-1 | (3n-2)(3n-1) | (18n-13)(3n-2) | A, AB, BP |
59 | 12 | 59 | 708 | 5n-1 | n | 5n-1 | n(5n-1) | B=kP |
59 | 12 | 60 | 590 | 48n-37 | 4(2n-1) | 4(4n-3)(2n-1) | 2(48n-37)(4n-3) | A, AB, BP |
59 | 14 | 35 | 590 | 48n-37 | 2(4n-1) | (4n-3)(4n-1) | 2(48n-37)(4n-3) | A, AB, BP |
59 | 15 | 30 | 590 | 120n-61 | 5(4n-1) | 10(2n-1)(4n-1) | 10(120n-61)(2n-1) | A, AB, BP |
59 | 20 | 20 | 590 | 6n-1 | 2n | 2n | n(6n-1) | A=B or B=C |
61 | 12 | 68 | 3111 | 54n-47 | 3(3n-2) | (15n-13)(3n-2) | 3(54n-47)(15n-13) | A, AB, BP |
61 | 16 | 28 | 6832 | 144n-83 | 8(3n-1) | (33n-19)(3n-1) | 8(144n-83)(33n-19) | A, AB, BP |
67 | 12 | 161 | 129444 | 144n-77 | 12(2n-1) | (346n-185)(2n-1) | 12(144n-77)(346n-185) | A, AB, BP |
67 | 12 | 162 | 21708 | 144n-77 | 12(2n-1) | 6(58n-31)(2n-1) | 12(144n-77)(58n-31) | A, AB, BP |
67 | 12 | 164 | 8241 | 54n-41 | 3(3n-2) | (33n-25)(3n-2) | 3(54n-41)(33n-25) | A, AB, BP |
67 | 12 | 168 | 3752 | 48n-29 | 4(2n-1) | 8(5n-3)(2n-1) | 8(48n-29)(5n-3) | A, AB, BP |
67 | 12 | 201 | 804 | 17n-1 | 3n | 3(17n-1) | 3n(17n-1) | B=kP |
67 | 12 | 268 | 402 | 23n-2 | 4n | 4(23n-2) | 2n(23n-2) | B=kP |
67 | 14 | 56 | 3752 | 168n-101 | 14(2n-1) | 28(5n-3)(2n-1) | 28(168n-101)(5n-3) | A, AB, BP |
67 | 16 | 37 | 39664 | 192n-125 | 16(2n-1) | (106n-69)(2n-1) | 16(192n-125)(106n-69) | A, AB, BP |
67 | 21 | 24 | 3752 | 168n-101 | 7(4n-1) | 4(5n-3)(4n-1) | 28(168n-101)(5n-3) | A, AB, BP |
71 | 12 | 853 | 726756 | 144n-73 | 12(2n-1) | (1730n-877)(2n-1) | 12(144n-73)(1730n-877) | A, AB, BP |
71 | 12 | 854 | 363804 | 144n-73 | 12(2n-1) | 2(866n-439)(2n-1) | 12(144n-73)(866n-439) | A, AB, BP |
71 | 12 | 855 | 242820 | 144n-73 | 12(2n-1) | 3(578n-293)(2n-1) | 12(144n-73)(578n-293) | A, AB, BP |
71 | 12 | 856 | 182328 | 108n-37 | 6(3n-1) | (651n-223)(3n-1) | 6(108n-37)(651n-223) | A, AB, BP |
71 | 12 | 858 | 121836 | 144n-73 | 12(2n-1) | 6(290n-147)(2n-1) | 12(144n-73)(290n-147) | A, AB, BP |
71 | 12 | 860 | 91590 | 108n-37 | 6(3n-1) | 2(327n-112)(3n-1) | 6(108n-37)(327n-112) | A, AB, BP |
71 | 12 | 861 | 81508 | 48n-25 | 4(2n-1) | (194n-101)(2n-1) | 4(48n-25)(194n-101) | A, AB, BP |
71 | 12 | 864 | 61344 | 108n-37 | 6(3n-1) | 9(73n-25)(3n-1) | 18(108n-37)(73n-25) | A, AB, BP |
71 | 12 | 868 | 46221 | 54n-37 | 3(3n-2) | (165n-113)(3n-2) | 3(54n-37)(165n-113) | A, AB, BP |
71 | 12 | 870 | 41180 | 48n-25 | 4(2n-1) | 2(98n-51)(2n-1) | 4(48n-25)(98n-51) | A, AB, BP |
71 | 12 | 876 | 31098 | 108n-37 | 6(3n-1) | 6(111n-38)(3n-1) | 6(108n-37)(111n-38) | A, AB, BP |
71 | 12 | 888 | 21016 | 48n-25 | 4(2n-1) | 8(25n-13)(2n-1) | 8(48n-25)(25n-13) | A, AB, BP |
71 | 12 | 900 | 15975 | 54n-37 | 3(3n-2) | 9(19n-13)(3n-2) | 9(54n-37)(19n-13) | A, AB, BP |
71 | 12 | 923 | 11076 | 77n-6 | 13n-1 | 13(77n-6) | 13(13n-1)(77n-6) | B=kP |
71 | 12 | 924 | 10934 | 48n-25 | 4(2n-1) | 4(52n-27)(2n-1) | 2(48n-25)(52n-27) | A, AB, BP |
71 | 12 | 994 | 5964 | 83n-12 | 2(7n-1) | 14(83n-12) | 14(7n-1)(83n-12) | B=kP |
71 | 12 | 996 | 5893 | 30n-19 | 5n-3 | (35n-22)(5n-3) | (30n-19)(35n-22) | A, AB, BP |
71 | 12 | 1065 | 4260 | 89n-18 | 3(5n-1) | 15(89n-18) | 15(5n-1)(89n-18) | B=kP |
71 | 12 | 1136 | 3408 | 95n-24 | 4(4n-1) | 16(95n-24) | 16(4n-1)(95n-24) | B=kP |
71 | 12 | 1278 | 2556 | 107n-36 | 6(3n-1) | 18(107n-36) | 18(3n-1)(107n-36) | B=kP |
71 | 12 | 1420 | 2130 | 119n-48 | 4(5n-2) | 20(119n-48) | 10(5n-2)(119n-48) | B=kP |
71 | 12 | 1491 | 1988 | 125n-54 | 3(7n-3) | 21(125n-54) | 7(7n-3)(125n-54) | B=kP |
71 | 12 | 1704 | 1704 | 6n-1 | n | 2n(6n-1) | 2n(6n-1) | A=B or B=C |
71 | 13 | 132 | 121836 | 156n-85 | 13(2n-1) | 2(145n-79)(2n-1) | 26(156n-85)(145n-79) | A, AB, BP |
71 | 13 | 142 | 1846 | 11n-6 | 2n-1 | 2(11n-6) | 2(2n-1)(11n-6) | B=kP |
71 | 13 | 156 | 852 | 30n-19 | 5n-2 | (5n-3)(5n-2) | (30n-19)(5n-3) | A, AB, BP |
71 | 14 | 77 | 10934 | 168n-97 | 14(2n-1) | 7(26n-15)(2n-1) | 14(168n-97)(26n-15) | A, AB, BP |
71 | 14 | 84 | 852 | 48n-25 | 2(4n-1) | 4(2n-1)(4n-1) | 4(48n-25)(2n-1) | A, AB, BP |
71 | 15 | 60 | 852 | 54n-37 | 3(3n-1) | 3(3n-2)(3n-1) | 3(54n-37)(3n-2) | A, AB, BP |
71 | 16 | 48 | 852 | 60n-49 | 2(5n-2) | (5n-4)(5n-2) | 2(60n-49)(5n-4) | A, AB, BP |
71 | 18 | 36 | 852 | 144n-73 | 6(4n-1) | 12(2n-1)(4n-1) | 12(144n-73)(2n-1) | A, AB, BP |
71 | 20 | 29 | 41180 | 240n-169 | 20(2n-1) | (98n-69)(2n-1) | 20(240n-169)(98n-69) | A, AB, BP |
71 | 20 | 30 | 852 | 144n-73 | 4(6n-1) | 6(2n-1)(6n-1) | 12(144n-73)(2n-1) | A, AB, BP |
71 | 21 | 28 | 852 | 144n-73 | 3(8n-1) | 4(2n-1)(8n-1) | 12(144n-73)(2n-1) | A, AB, BP |
71 | 24 | 24 | 852 | 6n-1 | 2n | 2n | n(6n-1) | A=B or B=C |
73 | 13 | 190 | 180310 | 156n-83 | 13(2n-1) | 2(203n-108)(2n-1) | 26(156n-83)(203n-108) | A, AB, BP |
73 | 14 | 93 | 95046 | 168n-95 | 14(2n-1) | (214n-121)(2n-1) | 14(168n-95)(214n-121) | A, AB, BP |
79 | 14 | 222 | 61383 | 126n-47 | 7(3n-1) | 3(59n-22)(3n-1) | 21(126n-47)(59n-22) | A, AB, BP |
79 | 14 | 224 | 17696 | 168n-89 | 14(2n-1) | 28(17n-9)(2n-1) | 28(168n-89)(17n-9) | A, AB, BP |
79 | 14 | 231 | 5214 | 24n-17 | 2(2n-1) | (10n-7)(2n-1) | 2(24n-17)(10n-7) | A, AB, BP |
79 | 14 | 237 | 3318 | 17n-6 | 3n-1 | 3(17n-6) | 3(3n-1)(17n-6) | B=kP |
79 | 15 | 108 | 42660 | 180n-101 | 15(2n-1) | 6(41n-23)(2n-1) | 30(180n-101)(41n-23) | A, AB, BP |
79 | 15 | 110 | 5214 | 36n-29 | 3(2n-1) | 2(5n-4)(2n-1) | 6(36n-29)(5n-4) | A, AB, BP |
79 | 16 | 79 | 1264 | 5n-1 | n | 5n-1 | n(5n-1) | B=kP |
79 | 22 | 33 | 5214 | 264n-185 | 22(2n-1) | 11(10n-7)(2n-1) | 22(264n-185)(10n-7) | A, AB, BP |
83 | 14 | 1163 | 1351406 | 168n-85 | 14(2n-1) | (2354n-1191)(2n-1) | 14(168n-85)(2354n-1191) | A, AB, BP |
83 | 14 | 1164 | 676284 | 168n-85 | 14(2n-1) | 4(589n-298)(2n-1) | 28(168n-85)(589n-298) | A, AB, BP |
83 | 14 | 1166 | 338723 | 126n-43 | 7(3n-1) | (885n-302)(3n-1) | 7(126n-43)(885n-302) | A, AB, BP |
83 | 14 | 1169 | 194054 | 168n-85 | 14(2n-1) | 7(338n-171)(2n-1) | 14(168n-85)(338n-171) | A, AB, BP |
83 | 14 | 1176 | 97608 | 168n-85 | 14(2n-1) | 28(85n-43)(2n-1) | 28(168n-85)(85n-43) | A, AB, BP |
83 | 14 | 1190 | 49385 | 126n-43 | 7(3n-1) | 7(129n-44)(3n-1) | 7(126n-43)(129n-44) | A, AB, BP |
83 | 14 | 1211 | 28718 | 24n-13 | 2(2n-1) | (50n-27)(2n-1) | 2(24n-13)(50n-27) | A, AB, BP |
83 | 14 | 1245 | 17430 | 89n-6 | 15n-1 | 15(89n-6) | 15(15n-1)(89n-6) | B=kP |
83 | 14 | 1260 | 14940 | 24n-13 | 2(2n-1) | 4(13n-7)(2n-1) | 4(24n-13)(13n-7) | A, AB, BP |
83 | 14 | 1328 | 9296 | 95n-12 | 2(8n-1) | 16(95n-12) | 16(8n-1)(95n-12) | B=kP |
83 | 14 | 1358 | 8051 | 18n-7 | 3n-1 | (21n-8)(3n-1) | (18n-7)(21n-8) | A, AB, BP |
83 | 14 | 1494 | 5229 | 107n-24 | 2(9n-2) | 18(107n-24) | 9(9n-2)(107n-24) | B=kP |
83 | 14 | 1743 | 3486 | 125n-42 | 7(3n-1) | 21(125n-42) | 21(3n-1)(125n-42) | B=kP |
83 | 14 | 2324 | 2324 | 6n-1 | n | 2n(6n-1) | 2n(6n-1) | A=B or B=C |
83 | 15 | 178 | 221610 | 180n-97 | 15(2n-1) | 2(193n-104)(2n-1) | 30(180n-97)(193n-104) | A, AB, BP |
83 | 15 | 180 | 14940 | 180n-97 | 15(2n-1) | 30(13n-7)(2n-1) | 30(180n-97)(13n-7) | A, AB, BP |
83 | 15 | 210 | 1162 | 24n-13 | 4n-1 | 2(2n-1)(4n-1) | 2(24n-13)(2n-1) | A, AB, BP |
83 | 16 | 112 | 1162 | 36n-25 | 2(3n-1) | 2(3n-2)(3n-1) | 2(36n-25)(3n-2) | A, AB, BP |
83 | 18 | 60 | 14940 | 216n-133 | 18(2n-1) | 12(13n-8)(2n-1) | 36(216n-133)(13n-8) | A, AB, BP |
83 | 18 | 63 | 1162 | 60n-37 | 2(5n-1) | (5n-3)(5n-1) | 2(60n-37)(5n-3) | A, AB, BP |
83 | 20 | 45 | 14940 | 240n-157 | 20(2n-1) | 5(26n-17)(2n-1) | 20(240n-157)(26n-17) | A, AB, BP |
83 | 21 | 42 | 1162 | 168n-85 | 7(4n-1) | 14(2n-1)(4n-1) | 14(168n-85)(2n-1) | A, AB, BP |
83 | 28 | 28 | 1162 | 6n-1 | 2n | 2n | n(6n-1) | A=B or B=C |
89 | 15 | 1336 | 1783560 | 180n-91 | 15(2n-1) | 2(1351n-683)(2n-1) | 30(180n-91)(1351n-683) | A, AB, BP |
89 | 15 | 1338 | 595410 | 180n-91 | 15(2n-1) | 6(451n-228)(2n-1) | 30(180n-91)(451n-228) | A, AB, BP |
89 | 15 | 1340 | 357780 | 180n-91 | 15(2n-1) | 10(271n-137)(2n-1) | 30(180n-91)(271n-137) | A, AB, BP |
89 | 15 | 1344 | 199360 | 60n-31 | 5(2n-1) | 2(151n-78)(2n-1) | 10(60n-31)(151n-78) | A, AB, BP |
89 | 15 | 1350 | 120150 | 180n-91 | 15(2n-1) | 30(91n-46)(2n-1) | 30(180n-91)(91n-46) | A, AB, BP |
89 | 15 | 1360 | 72624 | 36n-19 | 3(2n-1) | 2(55n-29)(2n-1) | 6(36n-19)(55n-29) | A, AB, BP |
89 | 15 | 1380 | 40940 | 60n-31 | 5(2n-1) | 10(31n-16)(2n-1) | 10(60n-31)(31n-16) | A, AB, BP |
89 | 15 | 1410 | 25098 | 36n-19 | 3(2n-1) | 6(19n-10)(2n-1) | 6(36n-19)(19n-10) | A, AB, BP |
89 | 15 | 1424 | 21360 | 95n-6 | 16n-1 | 16(95n-6) | 16(16n-1)(95n-6) | B=kP |
89 | 15 | 1560 | 9256 | 12n-7 | 2n-1 | 2(7n-4)(2n-1) | 2(12n-7)(7n-4) | A, AB, BP |
89 | 15 | 1602 | 8010 | 107n-18 | 3(6n-1) | 18(107n-18) | 18(6n-1)(107n-18) | B=kP |
89 | 15 | 1780 | 5340 | 119n-30 | 5(4n-1) | 20(119n-30) | 20(4n-1)(119n-30) | B=kP |
89 | 15 | 2136 | 3560 | 143n-54 | 3(8n-3) | 24(143n-54) | 8(8n-3)(143n-54) | B=kP |
89 | 15 | 2670 | 2670 | 6n-1 | n | 2n(6n-1) | 2n(6n-1) | A=B or B=C |
89 | 16 | 204 | 72624 | 144n-55 | 8(3n-1) | 3(55n-21)(3n-1) | 24(144n-55)(55n-21) | A, AB, BP |
89 | 16 | 208 | 9256 | 72n-55 | 4(3n-2) | 2(21n-16)(3n-2) | 4(72n-55)(21n-16) | A, AB, BP |
89 | 16 | 240 | 1335 | 36n-19 | 2(3n-1) | 6(2n-1)(3n-1) | 3(36n-19)(2n-1) | A, AB, BP |
89 | 18 | 89 | 1602 | 5n-1 | n | 5n-1 | n(5n-1) | B=kP |
89 | 18 | 90 | 1335 | 72n-55 | 6(2n-1) | 6(4n-3)(2n-1) | 3(72n-55)(4n-3) | A, AB, BP |
89 | 20 | 60 | 1335 | 150n-61 | 5(5n-1) | 5(5n-2)(5n-1) | 5(150n-61)(5n-2) | A, AB, BP |
89 | 24 | 39 | 9256 | 192n-103 | 8(4n-1) | (28n-15)(4n-1) | 8(192n-103)(28n-15) | A, AB, BP |
89 | 24 | 40 | 1335 | 162n-73 | 3(9n-1) | (9n-4)(9n-1) | 3(162n-73)(9n-4) | A, AB, BP |
89 | 30 | 30 | 1335 | 6n-1 | 2n | 2n | n(6n-1) | A=B or B=C |
97 | 17 | 330 | 544170 | 204n-107 | 17(2n-1) | 2(347n-182)(2n-1) | 34(204n-107)(347n-182) | A, AB, BP |
97 | 18 | 159 | 92538 | 216n-119 | 18(2n-1) | 3(118n-65)(2n-1) | 18(216n-119)(118n-65) | A, AB, BP |
97 | 18 | 162 | 7857 | 72n-47 | 6(2n-1) | 2(20n-13)(2n-1) | 3(72n-47)(20n-13) | A, AB, BP |
97 | 18 | 194 | 873 | 11n-2 | 2n | 2(11n-2) | n(11n-2) | B=kP |
97 | 22 | 61 | 130174 | 264n-167 | 22(2n-1) | (166n-105)(2n-1) | 22(264n-167)(166n-105) | A, AB, BP |
E-mail : kc2h-msm@asahi-net.or.jp三島 久典