11.解と恒等式の一覧表
7/p=1/a+1/b+1/c, final (53〜97)
p | a | b | c |
P | A | B | C |
type |
53 | 8 | 142 | 30104 | 112n-59 | 8(2n-1) | 2(150n-79)(2n-1) | 8(112n-59)(150n-79) | A, AB, BP |
53 | 8 | 144 | 7632 | 84n-31 | 4(3n-1) | 6(19n-7)(3n-1) | 12(84n-31)(19n-7) | A, AB, BP |
53 | 8 | 152 | 2014 | 42n-31 | 2(3n-2) | 2(15n-11)(3n-2) | 2(42n-31)(15n-11) | A, AB, BP |
53 | 8 | 159 | 1272 | 20n-7 | 3n-1 | 3(20n-7) | 3(3n-1)(20n-7) | B=kP |
53 | 8 | 212 | 424 | 27n-1 | 4n | 4(27n-1) | 4n(27n-1) | B=kP |
53 | 9 | 48 | 7632 | 126n-73 | 9(2n-1) | 6(19n-11)(2n-1) | 18(126n-73)(19n-11) | A, AB, BP |
53 | 9 | 53 | 477 | 6n-1 | n | 6n-1 | n(6n-1) | B=kP |
59 | 9 | 133 | 70623 | 126n-67 | 9(2n-1) | (284n-151)(2n-1) | 9(126n-67)(284n-151) | A, AB, BP |
59 | 9 | 135 | 7965 | 42n-25 | 3(2n-1) | (32n-19)(2n-1) | 3(42n-25)(32n-19) | A, AB, BP |
59 | 9 | 153 | 1003 | 14n-11 | 2n-1 | (4n-3)(2n-1) | (14n-11)(4n-3) | A, AB, BP |
59 | 9 | 177 | 531 | 20n-1 | 3n | 3(20n-1) | 3n(20n-1) | B=kP |
59 | 10 | 54 | 7965 | 105n-46 | 5(3n-1) | 3(16n-7)(3n-1) | 15(105n-46)(16n-7) | A, AB, BP |
59 | 10 | 59 | 590 | 6n-1 | n | 6n-1 | n(6n-1) | B=kP |
59 | 13 | 24 | 18408 | 182n-123 | 13(2n-1) | 2(37n-25)(2n-1) | 26(182n-123)(37n-25) | A, AB, BP |
59 | 17 | 17 | 1003 | 7n-4 | 2n-1 | 2n-1 | (2n-1)(7n-4) | A=B or B=C |
61 | 9 | 275 | 150975 | 126n-65 | 9(2n-1) | (568n-293)(2n-1) | 9(126n-65)(568n-293) | A, AB, BP |
61 | 9 | 276 | 50508 | 126n-65 | 9(2n-1) | 6(95n-49)(2n-1) | 18(126n-65)(95n-49) | A, AB, BP |
61 | 9 | 279 | 17019 | 42n-23 | 3(2n-1) | (64n-35)(2n-1) | 3(42n-23)(64n-35) | A, AB, BP |
61 | 9 | 288 | 5856 | 42n-23 | 3(2n-1) | 6(11n-6)(2n-1) | 6(42n-23)(11n-6) | A, AB, BP |
61 | 9 | 305 | 2745 | 34n-7 | 5n-1 | 5(34n-7) | 5(5n-1)(34n-7) | B=kP |
61 | 9 | 315 | 2135 | 14n-9 | 2n-1 | (8n-5)(2n-1) | (14n-9)(8n-5) | A, AB, BP |
61 | 9 | 366 | 1098 | 41n-21 | 3(2n-1) | 6(41n-21) | 6(2n-1)(41n-21) | B=kP |
61 | 9 | 549 | 549 | 7n-2 | n | n(7n-2) | n(7n-2) | A=B or B=C |
61 | 10 | 68 | 20740 | 140n-79 | 10(2n-1) | 4(39n-22)(2n-1) | 20(140n-79)(39n-22) | A, AB, BP |
61 | 10 | 70 | 2135 | 105n-44 | 5(3n-1) | 5(12n-5)(3n-1) | 5(105n-44)(12n-5) | A, AB, BP |
61 | 11 | 42 | 28182 | 154n-93 | 11(2n-1) | 2(53n-32)(2n-1) | 22(154n-93)(53n-32) | A, AB, BP |
61 | 12 | 32 | 5856 | 126n-65 | 6(3n-1) | (33n-17)(3n-1) | 6(126n-65)(33n-17) | A, AB, BP |
61 | 15 | 21 | 2135 | 140n-79 | 5(4n-1) | (16n-9)(4n-1) | 5(140n-79)(16n-9) | A, AB, BP |
67 | 10 | 224 | 75040 | 140n-73 | 10(2n-1) | 4(117n-61)(2n-1) | 20(140n-73)(117n-61) | A, AB, BP |
67 | 10 | 225 | 30150 | 140n-73 | 10(2n-1) | 5(94n-49)(2n-1) | 10(140n-73)(94n-49) | A, AB, BP |
67 | 10 | 230 | 7705 | 105n-38 | 5(3n-1) | 5(36n-13)(3n-1) | 5(105n-38)(36n-13) | A, AB, BP |
67 | 10 | 240 | 3216 | 28n-17 | 2(2n-1) | 4(5n-3)(2n-1) | 4(28n-17)(5n-3) | A, AB, BP |
67 | 10 | 268 | 1340 | 27n-14 | 2(2n-1) | 4(27n-14) | 4(2n-1)(27n-14) | B=kP |
67 | 10 | 335 | 670 | 34n-1 | 5n | 5(34n-1) | 5n(34n-1) | B=kP |
67 | 12 | 48 | 3216 | 126n-59 | 6(3n-1) | 3(15n-7)(3n-1) | 6(126n-59)(15n-7) | A, AB, BP |
67 | 16 | 24 | 3216 | 168n-101 | 8(3n-1) | 6(5n-3)(3n-1) | 24(168n-101)(5n-3) | A, AB, BP |
71 | 11 | 132 | 9372 | 154n-83 | 11(2n-1) | 22(13n-7)(2n-1) | 22(154n-83)(13n-7) | A, AB, BP |
71 | 11 | 142 | 1562 | 13n-7 | 2n-1 | 2(13n-7) | 2(2n-1)(13n-7) | B=kP |
71 | 12 | 66 | 9372 | 168n-97 | 12(2n-1) | 6(26n-15)(2n-1) | 12(168n-97)(26n-15) | A, AB, BP |
71 | 12 | 71 | 852 | 6n-1 | n | 6n-1 | n(6n-1) | B=kP |
73 | 11 | 201 | 161403 | 154n-81 | 11(2n-1) | (424n-223)(2n-1) | 11(154n-81)(424n-223) | A, AB, BP |
73 | 11 | 219 | 2409 | 20n-7 | 3n-1 | 3(20n-7) | 3(3n-1)(20n-7) | B=kP |
73 | 11 | 231 | 1533 | 14n-11 | 2n-1 | (4n-3)(2n-1) | (14n-11)(4n-3) | A, AB, BP |
73 | 12 | 80 | 17520 | 126n-53 | 6(3n-1) | (69n-29)(3n-1) | 6(126n-53)(69n-29) | A, AB, BP |
73 | 12 | 84 | 1533 | 63n-53 | 3(3n-2) | 3(6n-5)(3n-2) | 3(63n-53)(6n-5) | A, AB, BP |
73 | 14 | 42 | 1533 | 147n-74 | 7(3n-1) | 21(2n-1)(3n-1) | 21(147n-74)(2n-1) | A, AB, BP |
73 | 15 | 35 | 1533 | 63n-53 | 3(3n-1) | (6n-5)(3n-1) | 3(63n-53)(6n-5) | A, AB, BP |
73 | 16 | 30 | 17520 | 224n-151 | 16(2n-1) | 2(46n-31)(2n-1) | 16(224n-151)(46n-31) | A, AB, BP |
73 | 17 | 27 | 33507 | 238n-165 | 17(2n-1) | (88n-61)(2n-1) | 17(238n-165)(88n-61) | A, AB, BP |
73 | 21 | 21 | 1533 | 7n-4 | 2n-1 | 2n-1 | (2n-1)(7n-4) | A=B or B=C |
79 | 12 | 190 | 90060 | 168n-89 | 12(2n-1) | 2(202n-107)(2n-1) | 12(168n-89)(202n-107) | A, AB, BP |
79 | 12 | 192 | 15168 | 126n-47 | 6(3n-1) | 3(51n-19)(3n-1) | 6(126n-47)(51n-19) | A, AB, BP |
79 | 12 | 204 | 2686 | 56n-33 | 4(2n-1) | 4(12n-7)(2n-1) | 2(56n-33)(12n-7) | A, AB, BP |
79 | 12 | 237 | 948 | 20n-1 | 3n | 3(20n-1) | 3n(20n-1) | B=kP |
79 | 12 | 316 | 474 | 27n-2 | 4n | 4(27n-2) | 2n(27n-2) | B=kP |
79 | 17 | 34 | 2686 | 238n-159 | 17(2n-1) | 34(3n-2)(2n-1) | 34(238n-159)(3n-2) | A, AB, BP |
83 | 12 | 997 | 993012 | 168n-85 | 12(2n-1) | (2018n-1021)(2n-1) | 12(168n-85)(2018n-1021) | A, AB, BP |
83 | 12 | 998 | 497004 | 168n-85 | 12(2n-1) | 2(1010n-511)(2n-1) | 12(168n-85)(1010n-511) | A, AB, BP |
83 | 12 | 999 | 331668 | 168n-85 | 12(2n-1) | 3(674n-341)(2n-1) | 12(168n-85)(674n-341) | A, AB, BP |
83 | 12 | 1000 | 249000 | 126n-43 | 6(3n-1) | (759n-259)(3n-1) | 6(126n-43)(759n-259) | A, AB, BP |
83 | 12 | 1002 | 166332 | 168n-85 | 12(2n-1) | 6(338n-171)(2n-1) | 12(168n-85)(338n-171) | A, AB, BP |
83 | 12 | 1004 | 124998 | 126n-43 | 6(3n-1) | 2(381n-130)(3n-1) | 6(126n-43)(381n-130) | A, AB, BP |
83 | 12 | 1005 | 111220 | 56n-29 | 4(2n-1) | (226n-117)(2n-1) | 4(56n-29)(226n-117) | A, AB, BP |
83 | 12 | 1008 | 83664 | 126n-43 | 6(3n-1) | 9(85n-29)(3n-1) | 18(126n-43)(85n-29) | A, AB, BP |
83 | 12 | 1012 | 62997 | 63n-43 | 3(3n-2) | (192n-131)(3n-2) | 3(63n-43)(192n-131) | A, AB, BP |
83 | 12 | 1014 | 56108 | 56n-29 | 4(2n-1) | 2(114n-59)(2n-1) | 4(56n-29)(114n-59) | A, AB, BP |
83 | 12 | 1020 | 42330 | 126n-43 | 6(3n-1) | 6(129n-44)(3n-1) | 6(126n-43)(129n-44) | A, AB, BP |
83 | 12 | 1032 | 28552 | 56n-29 | 4(2n-1) | 8(29n-15)(2n-1) | 8(56n-29)(29n-15) | A, AB, BP |
83 | 12 | 1044 | 21663 | 63n-43 | 3(3n-2) | 9(22n-15)(3n-2) | 9(63n-43)(22n-15) | A, AB, BP |
83 | 12 | 1068 | 14774 | 56n-29 | 4(2n-1) | 4(60n-31)(2n-1) | 2(56n-29)(60n-31) | A, AB, BP |
83 | 12 | 1079 | 12948 | 90n-7 | 13n-1 | 13(90n-7) | 13(13n-1)(90n-7) | B=kP |
83 | 12 | 1140 | 7885 | 35n-22 | 5n-3 | 5(8n-5)(5n-3) | 5(35n-22)(8n-5) | A, AB, BP |
83 | 12 | 1162 | 6972 | 97n-14 | 2(7n-1) | 14(97n-14) | 14(7n-1)(97n-14) | B=kP |
83 | 12 | 1245 | 4980 | 104n-21 | 3(5n-1) | 15(104n-21) | 15(5n-1)(104n-21) | B=kP |
83 | 12 | 1328 | 3984 | 111n-28 | 4(4n-1) | 16(111n-28) | 16(4n-1)(111n-28) | B=kP |
83 | 12 | 1494 | 2988 | 125n-42 | 6(3n-1) | 18(125n-42) | 18(3n-1)(125n-42) | B=kP |
83 | 12 | 1660 | 2490 | 139n-56 | 4(5n-2) | 20(139n-56) | 10(5n-2)(139n-56) | B=kP |
83 | 12 | 1743 | 2324 | 146n-63 | 3(7n-3) | 21(146n-63) | 7(7n-3)(146n-63) | B=kP |
83 | 12 | 1992 | 1992 | 7n-1 | n | 2n(7n-1) | 2n(7n-1) | A=B or B=C |
83 | 13 | 135 | 145665 | 182n-99 | 13(2n-1) | (296n-161)(2n-1) | 13(182n-99)(296n-161) | A, AB, BP |
83 | 13 | 156 | 996 | 35n-22 | 5n-2 | (5n-3)(5n-2) | (35n-22)(5n-3) | A, AB, BP |
83 | 14 | 83 | 1162 | 6n-1 | n | 6n-1 | n(6n-1) | B=kP |
83 | 14 | 84 | 996 | 56n-29 | 2(4n-1) | 4(2n-1)(4n-1) | 4(56n-29)(2n-1) | A, AB, BP |
83 | 15 | 57 | 7885 | 70n-57 | 5(2n-1) | (16n-13)(2n-1) | 5(70n-57)(16n-13) | A, AB, BP |
83 | 15 | 60 | 996 | 63n-43 | 3(3n-1) | 3(3n-2)(3n-1) | 3(63n-43)(3n-2) | A, AB, BP |
83 | 16 | 48 | 996 | 70n-57 | 2(5n-2) | (5n-4)(5n-2) | 2(70n-57)(5n-4) | A, AB, BP |
83 | 18 | 36 | 996 | 168n-85 | 6(4n-1) | 12(2n-1)(4n-1) | 12(168n-85)(2n-1) | A, AB, BP |
83 | 20 | 30 | 996 | 168n-85 | 4(6n-1) | 6(2n-1)(6n-1) | 12(168n-85)(2n-1) | A, AB, BP |
83 | 21 | 28 | 996 | 168n-85 | 3(8n-1) | 4(2n-1)(8n-1) | 12(168n-85)(2n-1) | A, AB, BP |
83 | 24 | 24 | 996 | 7n-1 | 2n | 2n | n(7n-1) | A=B or B=C |
89 | 13 | 579 | 669903 | 182n-93 | 13(2n-1) | (1184n-605)(2n-1) | 13(182n-93)(1184n-605) | A, AB, BP |
89 | 13 | 585 | 52065 | 182n-93 | 13(2n-1) | 13(92n-47)(2n-1) | 13(182n-93)(92n-47) | A, AB, BP |
89 | 13 | 623 | 8099 | 48n-7 | 7n-1 | 7(48n-7) | 7(7n-1)(48n-7) | B=kP |
89 | 13 | 663 | 4539 | 14n-9 | 2n-1 | (8n-5)(2n-1) | (14n-9)(8n-5) | A, AB, BP |
89 | 13 | 1157 | 1157 | 7n-2 | n | n(7n-2) | n(7n-2) | A=B or B=C |
89 | 14 | 140 | 12460 | 196n-107 | 14(2n-1) | 28(11n-6)(2n-1) | 28(196n-107)(11n-6) | A, AB, BP |
89 | 14 | 178 | 623 | 13n-2 | 2n | 2(13n-2) | n(13n-2) | B=kP |
89 | 15 | 84 | 12460 | 70n-51 | 5(2n-1) | 2(11n-8)(2n-1) | 10(70n-51)(11n-8) | A, AB, BP |
89 | 15 | 85 | 4539 | 42n-37 | 3(2n-1) | (8n-7)(2n-1) | 3(42n-37)(8n-7) | A, AB, BP |
89 | 15 | 89 | 1335 | 6n-1 | n | 6n-1 | n(6n-1) | B=kP |
89 | 16 | 62 | 44144 | 224n-135 | 16(2n-1) | 2(78n-47)(2n-1) | 16(224n-135)(78n-47) | A, AB, BP |
89 | 17 | 51 | 4539 | 238n-149 | 17(2n-1) | 17(8n-5)(2n-1) | 17(238n-149)(8n-5) | A, AB, BP |
89 | 20 | 35 | 12460 | 280n-191 | 20(2n-1) | 5(22n-15)(2n-1) | 20(280n-191)(22n-15) | A, AB, BP |
97 | 14 | 1359 | 1845522 | 196n-99 | 14(2n-1) | (2746n-1387)(2n-1) | 14(196n-99)(2746n-1387) | A, AB, BP |
97 | 14 | 1360 | 923440 | 196n-99 | 14(2n-1) | 4(687n-347)(2n-1) | 28(196n-99)(687n-347) | A, AB, BP |
97 | 14 | 1362 | 462399 | 147n-50 | 7(3n-1) | 3(344n-117)(3n-1) | 21(147n-50)(344n-117) | A, AB, BP |
97 | 14 | 1365 | 264810 | 196n-99 | 14(2n-1) | 7(394n-199)(2n-1) | 14(196n-99)(394n-199) | A, AB, BP |
97 | 14 | 1372 | 133084 | 196n-99 | 14(2n-1) | 28(99n-50)(2n-1) | 28(196n-99)(99n-50) | A, AB, BP |
97 | 14 | 1386 | 67221 | 147n-50 | 7(3n-1) | 21(50n-17)(3n-1) | 21(147n-50)(50n-17) | A, AB, BP |
97 | 14 | 1407 | 38994 | 28n-15 | 2(2n-1) | (58n-31)(2n-1) | 2(28n-15)(58n-31) | A, AB, BP |
97 | 14 | 1455 | 20370 | 104n-7 | 15n-1 | 15(104n-7) | 15(15n-1)(104n-7) | B=kP |
97 | 14 | 1456 | 20176 | 28n-15 | 2(2n-1) | 4(15n-8)(2n-1) | 4(28n-15)(15n-8) | A, AB, BP |
97 | 14 | 1552 | 10864 | 111n-14 | 2(8n-1) | 16(111n-14) | 16(8n-1)(111n-14) | B=kP |
97 | 14 | 1554 | 10767 | 21n-8 | 3n-1 | 3(8n-3)(3n-1) | 3(21n-8)(8n-3) | A, AB, BP |
97 | 14 | 1746 | 6111 | 125n-28 | 2(9n-2) | 18(125n-28) | 9(9n-2)(125n-28) | B=kP |
97 | 14 | 2037 | 4074 | 146n-49 | 7(3n-1) | 21(146n-49) | 21(3n-1)(146n-49) | B=kP |
97 | 14 | 2716 | 2716 | 7n-1 | n | 2n(7n-1) | 2n(7n-1) | A=B or B=C |
97 | 15 | 182 | 264810 | 210n-113 | 15(2n-1) | 2(197n-106)(2n-1) | 30(210n-113)(197n-106) | A, AB, BP |
97 | 15 | 183 | 29585 | 70n-43 | 5(2n-1) | (44n-27)(2n-1) | 5(70n-43)(44n-27) | A, AB, BP |
97 | 15 | 185 | 10767 | 42n-29 | 3(2n-1) | (16n-11)(2n-1) | 3(42n-29)(16n-11) | A, AB, BP |
97 | 15 | 194 | 2910 | 13n-7 | 2n-1 | 2(13n-7) | 2(2n-1)(13n-7) | B=kP |
97 | 15 | 210 | 1358 | 28n-15 | 4n-1 | 2(2n-1)(4n-1) | 2(28n-15)(2n-1) | A, AB, BP |
97 | 15 | 291 | 485 | 20n-3 | 3n | 3(20n-3) | n(20n-3) | B=kP |
97 | 16 | 104 | 20176 | 168n-71 | 8(3n-1) | 2(45n-19)(3n-1) | 8(168n-71)(45n-19) | A, AB, BP |
97 | 16 | 112 | 1358 | 42n-29 | 2(3n-1) | 2(3n-2)(3n-1) | 2(42n-29)(3n-2) | A, AB, BP |
97 | 17 | 75 | 123675 | 238n-141 | 17(2n-1) | (184n-109)(2n-1) | 17(238n-141)(184n-109) | A, AB, BP |
97 | 18 | 63 | 1358 | 70n-43 | 2(5n-1) | (5n-3)(5n-1) | 2(70n-43)(5n-3) | A, AB, BP |
97 | 21 | 42 | 1358 | 196n-99 | 7(4n-1) | 14(2n-1)(4n-1) | 14(196n-99)(2n-1) | A, AB, BP |
97 | 28 | 28 | 1358 | 7n-1 | 2n | 2n | n(7n-1) | A=B or B=C |
E-mail : kc2h-msm@asahi-net.or.jp三島 久典