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