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11．解と恒等式の一覧表
5/p＝1/a＋1/b＋1/c, final (2〜47)
p a b c
P A B C
type
2 1 1 2 5n-3 2n-1 2n-1 (2n-1)(5n-3) A=B or B=C 3 1 2 6 10n-7 2n-1 2(3n-2)(2n-1) 2(10n-7)(3n-2) A, AB, BP 3 1 3 3 5n-2 n n(5n-2) n(5n-2) A=B or B=C 5 2 3 6 1 2 3 6 １の分割 5 2 4 4 1 2 4 4 １の分割 5 3 3 3 1 3 3 3 １の分割 7 2 5 70 20n-13 2(2n-1) (14n-9)(2n-1) 2(20n-13)(14n-9) A, AB, BP 7 2 6 21 15n-8 3n-1 3(2n-1)(3n-1) 3(15n-8)(2n-1) A, AB, BP 7 2 7 14 4n-1 n 4n-1 n(4n-1) B=kP 7 3 3 21 5n-3 2n-1 2n-1 (2n-1)(5n-3) A=B or B=C 11 3 9 99 30n-19 3(2n-1) 3(8n-5)(2n-1) 3(30n-19)(8n-5) A, AB, BP 11 3 11 33 4n-1 n 4n-1 n(4n-1) B=kP 11 4 5 220 40n-29 4(2n-1) (18n-13)(2n-1) 4(40n-29)(18n-13) A, AB, BP 13 3 20 780 30n-17 3(2n-1) 2(23n-13)(2n-1) 6(30n-17)(23n-13) A, AB, BP 13 3 21 273 30n-17 3(2n-1) 3(16n-9)(2n-1) 3(30n-17)(16n-9) A, AB, BP 13 3 24 104 10n-7 2n-1 2(3n-2)(2n-1) 2(10n-7)(3n-2) A, AB, BP 13 3 26 78 9n-5 2n-1 2(9n-5) 2(2n-1)(9n-5) B=kP 13 3 39 39 5n-2 n n(5n-2) n(5n-2) A=B or B=C 13 4 8 104 30n-17 2(3n-1) (9n-5)(3n-1) 2(30n-17)(9n-5) A, AB, BP 17 4 23 1564 40n-23 4(2n-1) (54n-31)(2n-1) 4(40n-23)(54n-31) A, AB, BP 17 4 24 408 30n-13 2(3n-1) 3(7n-3)(3n-1) 6(30n-13)(7n-3) A, AB, BP 17 4 28 119 15n-13 3n-2 (6n-5)(3n-2) (15n-13)(6n-5) A, AB, BP 17 4 34 68 9n-1 2n 2(9n-1) 2n(9n-1) B=kP 17 6 8 408 60n-43 6(2n-1) 4(7n-5)(2n-1) 12(60n-43)(7n-5) A, AB, BP 17 7 7 119 5n-3 2n-1 2n-1 (2n-1)(5n-3) A=B or B=C 19 4 77 5852 40n-21 4(2n-1) (162n-85)(2n-1) 4(40n-21)(162n-85) A, AB, BP 19 4 78 2964 40n-21 4(2n-1) 2(82n-43)(2n-1) 4(40n-21)(82n-43) A, AB, BP 19 4 80 1520 30n-11 2(3n-1) (63n-23)(3n-1) 2(30n-11)(63n-23) A, AB, BP 19 4 84 798 30n-11 2(3n-1) 6(11n-4)(3n-1) 6(30n-11)(11n-4) A, AB, BP 19 4 92 437 15n-11 3n-2 (18n-13)(3n-2) (15n-11)(18n-13) A, AB, BP 19 4 95 380 24n-5 5n-1 5(24n-5) 5(5n-1)(24n-5) B=kP 19 4 114 228 29n-10 2(3n-1) 6(29n-10) 6(3n-1)(29n-10) B=kP 19 4 152 152 5n-1 n 2n(5n-1) 2n(5n-1) A=B or B=C 19 5 16 1520 50n-31 5(2n-1) 2(21n-13)(2n-1) 10(50n-31)(21n-13) A, AB, BP 19 5 19 95 4n-1 n 4n-1 n(4n-1) B=kP 19 5 20 76 15n-11 3n-1 (3n-2)(3n-1) (15n-11)(3n-2) A, AB, BP 19 6 12 76 40n-21 2(4n-1) 4(2n-1)(4n-1) 4(40n-21)(2n-1) A, AB, BP 19 8 8 76 5n-1 2n 2n n(5n-1) A=B or B=C 23 5 58 6670 50n-27 5(2n-1) 2(63n-34)(2n-1) 10(50n-27)(63n-34) A, AB, BP 23 5 60 1380 50n-27 5(2n-1) 10(13n-7)(2n-1) 10(50n-27)(13n-7) A, AB, BP 23 5 69 345 14n-5 3n-1 3(14n-5) 3(3n-1)(14n-5) B=kP 23 5 70 322 10n-7 2n-1 2(3n-2)(2n-1) 2(10n-7)(3n-2) A, AB, BP 23 5 115 115 5n-2 n n(5n-2) n(5n-2) A=B or B=C 23 6 20 1380 60n-37 6(2n-1) 4(13n-8)(2n-1) 12(60n-37)(13n-8) A, AB, BP 23 6 21 322 20n-17 2(2n-1) (6n-5)(2n-1) 2(20n-17)(6n-5) A, AB, BP 23 6 23 138 4n-1 n 4n-1 n(4n-1) B=kP 23 7 14 322 70n-47 7(2n-1) 14(3n-2)(2n-1) 14(70n-47)(3n-2) A, AB, BP 29 6 175 30450 60n-31 6(2n-1) (362n-187)(2n-1) 6(60n-31)(362n-187) A, AB, BP 29 6 176 15312 60n-31 6(2n-1) 4(91n-47)(2n-1) 12(60n-31)(91n-47) A, AB, BP 29 6 177 10266 60n-31 6(2n-1) 3(122n-63)(2n-1) 6(60n-31)(122n-63) A, AB, BP 29 6 178 7743 45n-16 3(3n-1) (138n-49)(3n-1) 3(45n-16)(138n-49) A, AB, BP 29 6 180 5220 60n-31 6(2n-1) 12(31n-16)(2n-1) 12(60n-31)(31n-16) A, AB, BP 29 6 183 3538 20n-11 2(2n-1) (42n-23)(2n-1) 2(20n-11)(42n-23) A, AB, BP 29 6 186 2697 45n-16 3(3n-1) 3(48n-17)(3n-1) 3(45n-16)(48n-17) A, AB, BP 29 6 192 1856 20n-11 2(2n-1) 4(11n-6)(2n-1) 4(20n-11)(11n-6) A, AB, BP 29 6 203 1218 34n-5 7n-1 7(34n-5) 7(7n-1)(34n-5) B=kP 29 6 210 1015 20n-11 2(2n-1) 2(24n-13)(2n-1) (20n-11)(24n-13) A, AB, BP 29 6 232 696 39n-10 2(4n-1) 8(39n-10) 8(4n-1)(39n-10) B=kP 29 6 261 522 44n-15 3(3n-1) 9(44n-15) 9(3n-1)(44n-15) B=kP 29 6 290 435 49n-20 2(5n-2) 10(49n-20) 5(5n-2)(49n-20) B=kP 29 6 348 348 5n-1 n 2n(5n-1) 2n(5n-1) A=B or B=C 29 7 34 6902 70n-41 7(2n-1) 2(41n-24)(2n-1) 14(70n-41)(41n-24) A, AB, BP 29 7 35 1015 70n-41 7(2n-1) 7(12n-7)(2n-1) 7(70n-41)(12n-7) A, AB, BP 29 7 42 174 20n-11 4n-1 2(2n-1)(4n-1) 2(20n-11)(2n-1) A, AB, BP 29 8 24 174 50n-21 2(5n-1) 2(5n-2)(5n-1) 2(50n-21)(5n-2) A, AB, BP 29 9 18 174 60n-31 3(4n-1) 6(2n-1)(4n-1) 6(60n-31)(2n-1) A, AB, BP 29 10 14 1015 75n-46 5(3n-1) (18n-11)(3n-1) 5(75n-46)(18n-11) A, AB, BP 29 10 15 174 60n-31 2(6n-1) 3(2n-1)(6n-1) 6(60n-31)(2n-1) A, AB, BP 29 12 12 174 5n-1 2n 2n n(5n-1) A=B or B=C 31 7 56 1736 70n-39 7(2n-1) 14(9n-5)(2n-1) 14(70n-39)(9n-5) A, AB, BP 31 7 62 434 9n-5 2n-1 2(9n-5) 2(2n-1)(9n-5) B=kP 31 8 28 1736 60n-29 4(3n-1) (27n-13)(3n-1) 4(60n-29)(27n-13) A, AB, BP 31 8 31 248 4n-1 n 4n-1 n(4n-1) B=kP 31 9 20 5580 90n-59 9(2n-1) 2(29n-19)(2n-1) 18(90n-59)(29n-19) A, AB, BP 37 8 99 29304 80n-43 8(2n-1) (214n-115)(2n-1) 8(80n-43)(214n-115) A, AB, BP 37 8 100 7400 60n-23 4(3n-1) (81n-31)(3n-1) 4(60n-23)(81n-31) A, AB, BP 37 8 104 1924 30n-23 2(3n-2) (21n-16)(3n-2) 2(30n-23)(21n-16) A, AB, BP 37 8 111 888 14n-5 3n-1 3(14n-5) 3(3n-1)(14n-5) B=kP 37 8 120 555 15n-8 3n-1 3(2n-1)(3n-1) 3(15n-8)(2n-1) A, AB, BP 37 8 148 296 19n-1 4n 4(19n-1) 4n(19n-1) B=kP 37 9 42 4662 90n-53 9(2n-1) 6(17n-10)(2n-1) 18(90n-53)(17n-10) A, AB, BP 37 9 45 555 30n-23 3(2n-1) 3(4n-3)(2n-1) 3(30n-23)(4n-3) A, AB, BP 37 10 30 555 75n-38 5(3n-1) 15(2n-1)(3n-1) 15(75n-38)(2n-1) A, AB, BP 37 12 20 555 75n-38 3(5n-1) 5(2n-1)(5n-1) 15(75n-38)(2n-1) A, AB, BP 37 15 15 555 5n-3 2n-1 2n-1 (2n-1)(5n-3) A=B or B=C 41 9 93 11439 90n-49 9(2n-1) 3(68n-37)(2n-1) 9(90n-49)(68n-37) A, AB, BP 41 9 99 1353 30n-19 3(2n-1) 3(8n-5)(2n-1) 3(30n-19)(8n-5) A, AB, BP 41 9 123 369 14n-1 3n 3(14n-1) 3n(14n-1) B=kP 41 10 46 4715 75n-34 5(3n-1) (42n-19)(3n-1) 5(75n-34)(42n-19) A, AB, BP 41 11 33 1353 110n-69 11(2n-1) 11(8n-5)(2n-1) 11(110n-69)(8n-5) A, AB, BP 41 12 26 6396 120n-79 12(2n-1) 2(38n-25)(2n-1) 12(120n-79)(38n-25) A, AB, BP 43 9 194 75078 90n-47 9(2n-1) 2(203n-106)(2n-1) 18(90n-47)(203n-106) A, AB, BP 43 9 195 25155 90n-47 9(2n-1) 3(136n-71)(2n-1) 9(90n-47)(136n-71) A, AB, BP 43 9 198 8514 30n-17 3(2n-1) 2(23n-13)(2n-1) 6(30n-17)(23n-13) A, AB, BP 43 9 207 2967 30n-17 3(2n-1) 3(16n-9)(2n-1) 3(30n-17)(16n-9) A, AB, BP 43 9 215 1935 24n-5 5n-1 5(24n-5) 5(5n-1)(24n-5) B=kP 43 9 234 1118 10n-7 2n-1 2(3n-2)(2n-1) 2(10n-7)(3n-2) A, AB, BP 43 9 258 774 29n-15 3(2n-1) 6(29n-15) 6(2n-1)(29n-15) B=kP 43 9 387 387 5n-2 n n(5n-2) n(5n-2) A=B or B=C 43 10 62 6665 75n-32 5(3n-1) (54n-23)(3n-1) 5(75n-32)(54n-23) A, AB, BP 43 10 65 1118 20n-17 2(2n-1) (6n-5)(2n-1) 2(20n-17)(6n-5) A, AB, BP 43 10 86 215 9n-2 2n 2(9n-2) n(9n-2) B=kP 43 11 43 473 4n-1 n 4n-1 n(4n-1) B=kP 43 13 26 1118 130n-87 13(2n-1) 26(3n-2)(2n-1) 26(130n-87)(3n-2) A, AB, BP 47 10 157 73790 100n-53 10(2n-1) (334n-177)(2n-1) 10(100n-53)(334n-177) A, AB, BP 47 10 158 18565 75n-28 5(3n-1) (126n-47)(3n-1) 5(75n-28)(126n-47) A, AB, BP 47 10 160 7520 100n-53 10(2n-1) 20(17n-9)(2n-1) 20(100n-53)(17n-9) A, AB, BP 47 10 165 3102 20n-13 2(2n-1) (14n-9)(2n-1) 2(20n-13)(14n-9) A, AB, BP 47 10 188 940 19n-10 2(2n-1) 4(19n-10) 4(2n-1)(19n-10) B=kP 47 10 190 893 15n-13 3n-2 (6n-5)(3n-2) (15n-13)(6n-5) A, AB, BP 47 10 235 470 24n-1 5n 5(24n-1) 5n(24n-1) B=kP 47 11 66 3102 110n-63 11(2n-1) 22(7n-4)(2n-1) 22(110n-63)(7n-4) A, AB, BP 47 12 44 3102 90n-43 6(3n-1) 2(21n-10)(3n-1) 6(90n-43)(21n-10) A, AB, BP 47 12 47 564 4n-1 n 4n-1 n(4n-1) B=kP 47 13 34 20774 130n-83 13(2n-1) 2(47n-30)(2n-1) 26(130n-83)(47n-30) A, AB, BP 47 19 19 893 5n-3 2n-1 2n-1 (2n-1)(5n-3) A=B or B=C
E-mail : kc2h-msm@asahi-net.or.jp 三島 久典