１章 4/n=1/a+1/b+1/c

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１章 4/n=1/a+1/b+1/c

11．解と恒等式の一覧表

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)

4/p＝1/a＋1/b＋1/c, final (2～47)

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

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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