- 4/p＝1/a＋1/b＋1/c, final (2〜47), (53〜97)
- 5/p＝1/a＋1/b＋1/c, final (2〜47), (53〜97)
- 6/p＝1/a＋1/b＋1/c, final (2〜47), (53〜97)
- 7/p＝1/a＋1/b＋1/c, final (3〜47), (53〜97)

p | a | b | c | P | A | B | C | type |
---|---|---|---|---|---|---|---|---|

2 | 1 | 2 | 2 | 3n-1 | n | 3n-1 | n(3n-1) | B=kP |

3 | 1 | 4 | 12 | 8n-5 | 2n-1 | 2(5n-3)(2n-1) | 2(8n-5)(5n-3) | A, AB, BP |

3 | 1 | 6 | 6 | 4n-1 | n | 2n(4n-1) | 2n(4n-1) | A=B or B=C |

3 | 2 | 2 | 3 | 4n-1 | 2n | 2n | n(4n-1) | A=B or B=C |

5 | 2 | 4 | 20 | 16n-11 | 2(2n-1) | 4(3n-2)(2n-1) | 4(16n-11)(3n-2) | A, AB, BP |

5 | 2 | 5 | 10 | 3n-1 | n | 3n-1 | n(3n-1) | B=kP |

7 | 2 | 15 | 210 | 16n-9 | 2(2n-1) | (34n-19)(2n-1) | 2(16n-9)(34n-19) | A, AB, BP |

7 | 2 | 16 | 112 | 16n-9 | 2(2n-1) | 4(9n-5)(2n-1) | 4(16n-9)(9n-5) | A, AB, BP |

7 | 2 | 18 | 63 | 12n-5 | 3n-1 | 3(5n-2)(3n-1) | 3(12n-5)(5n-2) | A, AB, BP |

7 | 2 | 21 | 42 | 11n-4 | 3n-1 | 3(11n-4) | 3(3n-1)(11n-4) | B=kP |

7 | 2 | 28 | 28 | 4n-1 | n | 2n(4n-1) | 2n(4n-1) | A=B or B=C |

7 | 3 | 6 | 14 | 16n-9 | 4n-1 | 2(2n-1)(4n-1) | 2(16n-9)(2n-1) | A, AB, BP |

7 | 4 | 4 | 14 | 4n-1 | 2n | 2n | n(4n-1) | A=B or B=C |

11 | 3 | 34 | 1122 | 24n-13 | 3(2n-1) | 2(37n-20)(2n-1) | 6(24n-13)(37n-20) | A, AB, BP |

11 | 3 | 36 | 396 | 24n-13 | 3(2n-1) | 6(13n-7)(2n-1) | 6(24n-13)(13n-7) | A, AB, BP |

11 | 3 | 42 | 154 | 8n-5 | 2n-1 | 2(5n-3)(2n-1) | 2(8n-5)(5n-3) | A, AB, BP |

11 | 3 | 44 | 132 | 15n-4 | 4n-1 | 4(15n-4) | 4(4n-1)(15n-4) | B=kP |

11 | 3 | 66 | 66 | 4n-1 | n | 2n(4n-1) | 2n(4n-1) | A=B or B=C |

11 | 4 | 9 | 396 | 32n-21 | 4(2n-1) | (26n-17)(2n-1) | 4(32n-21)(26n-17) | A, AB, BP |

11 | 4 | 11 | 44 | 3n-1 | n | 3n-1 | n(3n-1) | B=kP |

11 | 4 | 12 | 33 | 20n-9 | 5n-1 | (5n-2)(5n-1) | (20n-9)(5n-2) | A, AB, BP |

11 | 6 | 6 | 33 | 4n-1 | 2n | 2n | n(4n-1) | A=B or B=C |

13 | 4 | 18 | 468 | 32n-19 | 4(2n-1) | 2(22n-13)(2n-1) | 4(32n-19)(22n-13) | A, AB, BP |

13 | 4 | 20 | 130 | 24n-11 | 2(3n-1) | 2(9n-4)(3n-1) | 2(24n-11)(9n-4) | A, AB, BP |

13 | 4 | 26 | 52 | 7n-1 | 2n | 2(7n-1) | 2n(7n-1) | B=kP |

13 | 5 | 10 | 130 | 40n-27 | 5(2n-1) | 10(3n-2)(2n-1) | 10(40n-27)(3n-2) | A, AB, BP |

17 | 5 | 30 | 510 | 40n-23 | 5(2n-1) | 10(7n-4)(2n-1) | 10(40n-23)(7n-4) | A, AB, BP |

17 | 5 | 34 | 170 | 7n-4 | 2n-1 | 2(7n-4) | 2(2n-1)(7n-4) | B=kP |

17 | 6 | 15 | 510 | 48n-31 | 6(2n-1) | 3(14n-9)(2n-1) | 6(48n-31)(14n-9) | A, AB, BP |

17 | 6 | 17 | 102 | 3n-1 | n | 3n-1 | n(3n-1) | B=kP |

19 | 5 | 96 | 9120 | 40n-21 | 5(2n-1) | 2(101n-53)(2n-1) | 10(40n-21)(101n-53) | A, AB, BP |

19 | 5 | 100 | 1900 | 40n-21 | 5(2n-1) | 10(21n-11)(2n-1) | 10(40n-21)(21n-11) | A, AB, BP |

19 | 5 | 114 | 570 | 23n-4 | 6n-1 | 6(23n-4) | 6(6n-1)(23n-4) | B=kP |

19 | 5 | 120 | 456 | 8n-5 | 2n-1 | 2(5n-3)(2n-1) | 2(8n-5)(5n-3) | A, AB, BP |

19 | 5 | 190 | 190 | 4n-1 | n | 2n(4n-1) | 2n(4n-1) | A=B or B=C |

19 | 6 | 23 | 2622 | 48n-29 | 6(2n-1) | (58n-35)(2n-1) | 6(48n-29)(58n-35) | A, AB, BP |

19 | 6 | 24 | 456 | 48n-29 | 6(2n-1) | 12(5n-3)(2n-1) | 12(48n-29)(5n-3) | A, AB, BP |

19 | 6 | 30 | 95 | 16n-13 | 2(2n-1) | 2(4n-3)(2n-1) | (16n-13)(4n-3) | A, AB, BP |

19 | 6 | 38 | 57 | 7n-2 | 2n | 2(7n-2) | n(7n-2) | B=kP |

19 | 8 | 12 | 456 | 48n-29 | 4(3n-1) | 3(5n-3)(3n-1) | 12(48n-29)(5n-3) | A, AB, BP |

19 | 10 | 10 | 95 | 4n-1 | 2n | 2n | n(4n-1) | A=B or B=C |

23 | 6 | 139 | 19182 | 48n-25 | 6(2n-1) | (290n-151)(2n-1) | 6(48n-25)(290n-151) | A, AB, BP |

23 | 6 | 140 | 9660 | 48n-25 | 6(2n-1) | 4(73n-38)(2n-1) | 12(48n-25)(73n-38) | A, AB, BP |

23 | 6 | 141 | 6486 | 48n-25 | 6(2n-1) | 3(98n-51)(2n-1) | 6(48n-25)(98n-51) | A, AB, BP |

23 | 6 | 142 | 4899 | 36n-13 | 3(3n-1) | (111n-40)(3n-1) | 3(36n-13)(111n-40) | A, AB, BP |

23 | 6 | 144 | 3312 | 48n-25 | 6(2n-1) | 12(25n-13)(2n-1) | 12(48n-25)(25n-13) | A, AB, BP |

23 | 6 | 147 | 2254 | 16n-9 | 2(2n-1) | (34n-19)(2n-1) | 2(16n-9)(34n-19) | A, AB, BP |

23 | 6 | 150 | 1725 | 36n-13 | 3(3n-1) | 3(39n-14)(3n-1) | 3(36n-13)(39n-14) | A, AB, BP |

23 | 6 | 156 | 1196 | 16n-9 | 2(2n-1) | 4(9n-5)(2n-1) | 4(16n-9)(9n-5) | A, AB, BP |

23 | 6 | 161 | 966 | 27n-4 | 7n-1 | 7(27n-4) | 7(7n-1)(27n-4) | B=kP |

23 | 6 | 174 | 667 | 16n-9 | 2(2n-1) | 2(20n-11)(2n-1) | (16n-9)(20n-11) | A, AB, BP |

23 | 6 | 184 | 552 | 31n-8 | 2(4n-1) | 8(31n-8) | 8(4n-1)(31n-8) | B=kP |

23 | 6 | 207 | 414 | 35n-12 | 3(3n-1) | 9(35n-12) | 9(3n-1)(35n-12) | B=kP |

23 | 6 | 230 | 345 | 39n-16 | 2(5n-2) | 10(39n-16) | 5(5n-2)(39n-16) | B=kP |

23 | 6 | 276 | 276 | 4n-1 | n | 2n(4n-1) | 2n(4n-1) | A=B or B=C |

23 | 7 | 42 | 138 | 16n-9 | 4n-1 | 2(2n-1)(4n-1) | 2(16n-9)(2n-1) | A, AB, BP |

23 | 8 | 23 | 184 | 3n-1 | n | 3n-1 | n(3n-1) | B=kP |

23 | 8 | 24 | 138 | 40n-17 | 2(5n-1) | 2(5n-2)(5n-1) | 2(40n-17)(5n-2) | A, AB, BP |

23 | 9 | 16 | 3312 | 72n-49 | 9(2n-1) | 2(25n-17)(2n-1) | 18(72n-49)(25n-17) | A, AB, BP |

23 | 9 | 18 | 138 | 48n-25 | 3(4n-1) | 6(2n-1)(4n-1) | 6(48n-25)(2n-1) | A, AB, BP |

23 | 10 | 15 | 138 | 48n-25 | 2(6n-1) | 3(2n-1)(6n-1) | 6(48n-25)(2n-1) | A, AB, BP |

23 | 12 | 12 | 138 | 4n-1 | 2n | 2n | n(4n-1) | A=B or B=C |

29 | 8 | 78 | 9048 | 64n-35 | 8(2n-1) | 2(86n-47)(2n-1) | 8(64n-35)(86n-47) | A, AB, BP |

29 | 8 | 80 | 2320 | 48n-19 | 4(3n-1) | 2(33n-13)(3n-1) | 4(48n-19)(33n-13) | A, AB, BP |

29 | 8 | 87 | 696 | 11n-4 | 3n-1 | 3(11n-4) | 3(3n-1)(11n-4) | B=kP |

29 | 8 | 88 | 638 | 24n-19 | 2(3n-2) | 2(9n-7)(3n-2) | 2(24n-19)(9n-7) | A, AB, BP |

29 | 8 | 116 | 232 | 15n-1 | 4n | 4(15n-1) | 4n(15n-1) | B=kP |

29 | 10 | 29 | 290 | 3n-1 | n | 3n-1 | n(3n-1) | B=kP |

29 | 11 | 22 | 638 | 88n-59 | 11(2n-1) | 22(3n-2)(2n-1) | 22(88n-59)(3n-2) | A, AB, BP |

31 | 8 | 249 | 61752 | 64n-33 | 8(2n-1) | (514n-265)(2n-1) | 8(64n-33)(514n-265) | A, AB, BP |

31 | 8 | 250 | 31000 | 64n-33 | 8(2n-1) | 2(258n-133)(2n-1) | 8(64n-33)(258n-133) | A, AB, BP |

31 | 8 | 252 | 15624 | 48n-17 | 4(3n-1) | 3(65n-23)(3n-1) | 12(48n-17)(65n-23) | A, AB, BP |

31 | 8 | 256 | 7936 | 48n-17 | 4(3n-1) | 2(99n-35)(3n-1) | 4(48n-17)(99n-35) | A, AB, BP |

31 | 8 | 264 | 4092 | 24n-17 | 2(3n-2) | 3(17n-12)(3n-2) | 6(24n-17)(17n-12) | A, AB, BP |

31 | 8 | 279 | 2232 | 35n-4 | 9n-1 | 9(35n-4) | 9(9n-1)(35n-4) | B=kP |

31 | 8 | 280 | 2170 | 24n-17 | 2(3n-2) | 2(27n-19)(3n-2) | 2(24n-17)(27n-19) | A, AB, BP |

31 | 8 | 310 | 1240 | 39n-8 | 2(5n-1) | 10(39n-8) | 10(5n-1)(39n-8) | B=kP |

31 | 8 | 312 | 1209 | 12n-5 | 3n-1 | 3(5n-2)(3n-1) | 3(12n-5)(5n-2) | A, AB, BP |

31 | 8 | 372 | 744 | 47n-16 | 4(3n-1) | 12(47n-16) | 12(3n-1)(47n-16) | B=kP |

31 | 8 | 496 | 496 | 4n-1 | n | 2n(4n-1) | 2n(4n-1) | A=B or B=C |

31 | 9 | 56 | 15624 | 72n-41 | 9(2n-1) | 2(65n-37)(2n-1) | 18(72n-41)(65n-37) | A, AB, BP |

31 | 9 | 62 | 558 | 7n-4 | 2n-1 | 2(7n-4) | 2(2n-1)(7n-4) | B=kP |

31 | 9 | 72 | 248 | 20n-9 | 5n-1 | (5n-2)(5n-1) | (20n-9)(5n-2) | A, AB, BP |

31 | 10 | 35 | 2170 | 80n-49 | 10(2n-1) | 5(18n-11)(2n-1) | 10(80n-49)(18n-11) | A, AB, BP |

31 | 10 | 40 | 248 | 24n-17 | 2(3n-1) | 2(3n-2)(3n-1) | 2(24n-17)(3n-2) | A, AB, BP |

31 | 12 | 22 | 4092 | 96n-65 | 12(2n-1) | 2(34n-23)(2n-1) | 12(96n-65)(34n-23) | A, AB, BP |

31 | 12 | 24 | 248 | 56n-25 | 2(7n-1) | (7n-3)(7n-1) | 2(56n-25)(7n-3) | A, AB, BP |

31 | 16 | 16 | 248 | 4n-1 | 2n | 2n | n(4n-1) | A=B or B=C |

37 | 10 | 124 | 22940 | 80n-43 | 10(2n-1) | 4(67n-36)(2n-1) | 20(80n-43)(67n-36) | A, AB, BP |

37 | 10 | 125 | 9250 | 80n-43 | 10(2n-1) | 5(54n-29)(2n-1) | 10(80n-43)(54n-29) | A, AB, BP |

37 | 10 | 130 | 2405 | 60n-23 | 5(3n-1) | 5(21n-8)(3n-1) | 5(60n-23)(21n-8) | A, AB, BP |

37 | 10 | 140 | 1036 | 16n-11 | 2(2n-1) | 4(3n-2)(2n-1) | 4(16n-11)(3n-2) | A, AB, BP |

37 | 10 | 148 | 740 | 15n-8 | 2(2n-1) | 4(15n-8) | 4(2n-1)(15n-8) | B=kP |

37 | 10 | 185 | 370 | 19n-1 | 5n | 5(19n-1) | 5n(19n-1) | B=kP |

37 | 12 | 42 | 1036 | 32n-27 | 4(2n-1) | 2(6n-5)(2n-1) | 4(32n-27)(6n-5) | A, AB, BP |

37 | 14 | 28 | 1036 | 112n-75 | 14(2n-1) | 28(3n-2)(2n-1) | 28(112n-75)(3n-2) | A, AB, BP |

37 | 16 | 22 | 6512 | 128n-91 | 16(2n-1) | 2(38n-27)(2n-1) | 16(128n-91)(38n-27) | A, AB, BP |

41 | 11 | 154 | 6314 | 88n-47 | 11(2n-1) | 22(15n-8)(2n-1) | 22(88n-47)(15n-8) | A, AB, BP |

41 | 11 | 164 | 1804 | 15n-4 | 4n-1 | 4(15n-4) | 4(4n-1)(15n-4) | B=kP |

41 | 12 | 72 | 2952 | 72n-31 | 6(3n-1) | 9(7n-3)(3n-1) | 18(72n-31)(7n-3) | A, AB, BP |

41 | 12 | 82 | 492 | 7n-1 | 2n | 2(7n-1) | 2n(7n-1) | B=kP |

41 | 12 | 123 | 164 | 11n-3 | 3n | 3(11n-3) | n(11n-3) | B=kP |

41 | 14 | 41 | 574 | 3n-1 | n | 3n-1 | n(3n-1) | B=kP |

41 | 18 | 24 | 2952 | 144n-103 | 18(2n-1) | 12(7n-5)(2n-1) | 36(144n-103)(7n-5) | A, AB, BP |

43 | 11 | 474 | 224202 | 88n-45 | 11(2n-1) | 2(485n-248)(2n-1) | 22(88n-45)(485n-248) | A, AB, BP |

43 | 11 | 484 | 20812 | 88n-45 | 11(2n-1) | 22(45n-23)(2n-1) | 22(88n-45)(45n-23) | A, AB, BP |

43 | 11 | 516 | 5676 | 47n-4 | 12n-1 | 12(47n-4) | 12(12n-1)(47n-4) | B=kP |

43 | 11 | 594 | 2322 | 8n-5 | 2n-1 | 2(5n-3)(2n-1) | 2(8n-5)(5n-3) | A, AB, BP |

43 | 11 | 946 | 946 | 4n-1 | n | 2n(4n-1) | 2n(4n-1) | A=B or B=C |

43 | 12 | 104 | 13416 | 72n-29 | 6(3n-1) | (87n-35)(3n-1) | 6(72n-29)(87n-35) | A, AB, BP |

43 | 12 | 105 | 6020 | 32n-21 | 4(2n-1) | (26n-17)(2n-1) | 4(32n-21)(26n-17) | A, AB, BP |

43 | 12 | 108 | 2322 | 72n-29 | 6(3n-1) | 18(5n-2)(3n-1) | 18(72n-29)(5n-2) | A, AB, BP |

43 | 12 | 129 | 516 | 11n-1 | 3n | 3(11n-1) | 3n(11n-1) | B=kP |

43 | 12 | 132 | 473 | 20n-17 | 5n-3 | (5n-4)(5n-3) | (20n-17)(5n-4) | A, AB, BP |

43 | 12 | 172 | 258 | 15n-2 | 4n | 4(15n-2) | 2n(15n-2) | B=kP |

43 | 15 | 38 | 24510 | 120n-77 | 15(2n-1) | 2(53n-34)(2n-1) | 30(120n-77)(53n-34) | A, AB, BP |

43 | 18 | 27 | 2322 | 96n-53 | 6(4n-1) | (20n-11)(4n-1) | 6(96n-53)(20n-11) | A, AB, BP |

43 | 22 | 22 | 473 | 4n-1 | 2n | 2n | n(4n-1) | A=B or B=C |

47 | 12 | 565 | 318660 | 96n-49 | 12(2n-1) | (1154n-589)(2n-1) | 12(96n-49)(1154n-589) | A, AB, BP |

47 | 12 | 566 | 159612 | 96n-49 | 12(2n-1) | 2(578n-295)(2n-1) | 12(96n-49)(578n-295) | A, AB, BP |

47 | 12 | 567 | 106596 | 96n-49 | 12(2n-1) | 3(386n-197)(2n-1) | 12(96n-49)(386n-197) | A, AB, BP |

47 | 12 | 568 | 80088 | 72n-25 | 6(3n-1) | (435n-151)(3n-1) | 6(72n-25)(435n-151) | A, AB, BP |

47 | 12 | 570 | 53580 | 96n-49 | 12(2n-1) | 6(194n-99)(2n-1) | 12(96n-49)(194n-99) | A, AB, BP |

47 | 12 | 572 | 40326 | 72n-25 | 6(3n-1) | 2(219n-76)(3n-1) | 6(72n-25)(219n-76) | A, AB, BP |

47 | 12 | 573 | 35908 | 32n-17 | 4(2n-1) | (130n-69)(2n-1) | 4(32n-17)(130n-69) | A, AB, BP |

47 | 12 | 576 | 27072 | 72n-25 | 6(3n-1) | 9(49n-17)(3n-1) | 18(72n-25)(49n-17) | A, AB, BP |

47 | 12 | 580 | 20445 | 36n-25 | 3(3n-2) | (111n-77)(3n-2) | 3(36n-25)(111n-77) | A, AB, BP |

47 | 12 | 582 | 18236 | 32n-17 | 4(2n-1) | 2(66n-35)(2n-1) | 4(32n-17)(66n-35) | A, AB, BP |

47 | 12 | 588 | 13818 | 72n-25 | 6(3n-1) | 6(75n-26)(3n-1) | 6(72n-25)(75n-26) | A, AB, BP |

47 | 12 | 600 | 9400 | 32n-17 | 4(2n-1) | 8(17n-9)(2n-1) | 8(32n-17)(17n-9) | A, AB, BP |

47 | 12 | 611 | 7332 | 51n-4 | 13n-1 | 13(51n-4) | 13(13n-1)(51n-4) | B=kP |

47 | 12 | 612 | 7191 | 36n-25 | 3(3n-2) | 9(13n-9)(3n-2) | 9(36n-25)(13n-9) | A, AB, BP |

47 | 12 | 636 | 4982 | 32n-17 | 4(2n-1) | 4(36n-19)(2n-1) | 2(32n-17)(36n-19) | A, AB, BP |

47 | 12 | 658 | 3948 | 55n-8 | 2(7n-1) | 14(55n-8) | 14(7n-1)(55n-8) | B=kP |

47 | 12 | 705 | 2820 | 59n-12 | 3(5n-1) | 15(59n-12) | 15(5n-1)(59n-12) | B=kP |

47 | 12 | 708 | 2773 | 20n-13 | 5n-3 | (25n-16)(5n-3) | (20n-13)(25n-16) | A, AB, BP |

47 | 12 | 752 | 2256 | 63n-16 | 4(4n-1) | 16(63n-16) | 16(4n-1)(63n-16) | B=kP |

47 | 12 | 846 | 1692 | 71n-24 | 6(3n-1) | 18(71n-24) | 18(3n-1)(71n-24) | B=kP |

47 | 12 | 940 | 1410 | 79n-32 | 4(5n-2) | 20(79n-32) | 10(5n-2)(79n-32) | B=kP |

47 | 12 | 987 | 1316 | 83n-36 | 3(7n-3) | 21(83n-36) | 7(7n-3)(83n-36) | B=kP |

47 | 12 | 1128 | 1128 | 4n-1 | n | 2n(4n-1) | 2n(4n-1) | A=B or B=C |

47 | 13 | 156 | 564 | 20n-13 | 5n-2 | (5n-3)(5n-2) | (20n-13)(5n-3) | A, AB, BP |

47 | 14 | 84 | 564 | 32n-17 | 2(4n-1) | 4(2n-1)(4n-1) | 4(32n-17)(2n-1) | A, AB, BP |

47 | 14 | 94 | 329 | 7n-2 | 2n | 2(7n-2) | n(7n-2) | B=kP |

47 | 15 | 60 | 564 | 36n-25 | 3(3n-1) | 3(3n-2)(3n-1) | 3(36n-25)(3n-2) | A, AB, BP |

47 | 16 | 47 | 752 | 3n-1 | n | 3n-1 | n(3n-1) | B=kP |

47 | 16 | 48 | 564 | 40n-33 | 2(5n-2) | (5n-4)(5n-2) | 2(40n-33)(5n-4) | A, AB, BP |

47 | 18 | 34 | 7191 | 108n-61 | 9(3n-1) | (39n-22)(3n-1) | 9(108n-61)(39n-22) | A, AB, BP |

47 | 18 | 36 | 564 | 96n-49 | 6(4n-1) | 12(2n-1)(4n-1) | 12(96n-49)(2n-1) | A, AB, BP |

47 | 20 | 30 | 564 | 96n-49 | 4(6n-1) | 6(2n-1)(6n-1) | 12(96n-49)(2n-1) | A, AB, BP |

47 | 21 | 28 | 564 | 96n-49 | 3(8n-1) | 4(2n-1)(8n-1) | 12(96n-49)(2n-1) | A, AB, BP |

47 | 24 | 24 | 564 | 4n-1 | 2n | 2n | n(4n-1) | A=B or B=C |

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E-mail : kc2h-msm@asahi-net.or.jp三島 久典