## 11．解と恒等式の一覧表

### 4/p＝1/a＋1/b＋1/c, final (53〜97)

pabc PABC type
5314265371019n-45n-15(19n-4)5(5n-1)(19n-4)B=kP
5314280212016n-112(2n-1)4(3n-2)(2n-1)4(16n-11)(3n-2)A, AB, BP
5314318111323n-162(3n-2)6(23n-16)3(3n-2)(23n-16)B=kP
531437174227n-17n7(27n-1)7n(27n-1)B=kP
531511430210120n-6715(2n-1)6(43n-24)(2n-1)30(120n-67)(43n-24)A, AB, BP
5315120212040n-275(2n-1)10(3n-2)(2n-1)10(40n-27)(3n-2)A, AB, BP
531680212048n-434(3n-2)2(9n-8)(3n-2)4(48n-43)(9n-8)A, AB, BP
5318539543n-1n3n-1n(3n-1)B=kP
5320402120120n-6710(3n-1)5(9n-5)(3n-1)10(120n-67)(9n-5)A, AB, BP
53213613356168n-11521(2n-1)6(19n-13)(2n-1)42(168n-115)(19n-13)A, AB, BP
5324302120128n-758(4n-1)2(12n-7)(4n-1)8(128n-75)(12n-7)A, AB, BP
5915886784110120n-6115(2n-1)2(901n-458)(2n-1)30(120n-61)(901n-458)A, AB, BP
5915888261960120n-6115(2n-1)6(301n-153)(2n-1)30(120n-61)(301n-153)A, AB, BP
5915890157530120n-6115(2n-1)10(181n-92)(2n-1)30(120n-61)(181n-92)A, AB, BP
59158948791040n-215(2n-1)2(101n-53)(2n-1)10(40n-21)(101n-53)A, AB, BP
591590053100120n-6115(2n-1)30(61n-31)(2n-1)30(120n-61)(61n-31)A, AB, BP
59159103221424n-133(2n-1)2(37n-20)(2n-1)6(24n-13)(37n-20)A, AB, BP
59159301829040n-215(2n-1)10(21n-11)(2n-1)10(40n-21)(21n-11)A, AB, BP
59159441416063n-416n-116(63n-4)16(16n-1)(63n-4)B=kP
59159601132824n-133(2n-1)6(13n-7)(2n-1)6(24n-13)(13n-7)A, AB, BP
59151062531071n-123(6n-1)18(71n-12)18(6n-1)(71n-12)B=kP
5915111043668n-52n-12(5n-3)(2n-1)2(8n-5)(5n-3)A, AB, BP
59151180354079n-205(4n-1)20(79n-20)20(4n-1)(79n-20)B=kP
59151416236095n-363(8n-3)24(95n-36)8(8n-3)(95n-36)B=kP
5915177017704n-1n2n(4n-1)2n(4n-1)A=B or B=C
5916189178416128n-6916(2n-1)(410n-221)(2n-1)16(128n-69)(410n-221)A, AB, BP
59161921132848n-374(3n-2)3(13n-10)(3n-2)12(48n-37)(13n-10)A, AB, BP
591623694415n-14n4(15n-1)4n(15n-1)B=kP
591624088524n-132(3n-1)6(2n-1)(3n-1)3(24n-13)(2n-1)A, AB, BP
591711820067n-42n-12(7n-4)2(2n-1)(7n-4)B=kP
59188221771108n-499(3n-1)(75n-34)(3n-1)9(108n-49)(75n-34)A, AB, BP
59189088548n-376(2n-1)6(4n-3)(2n-1)3(48n-37)(4n-3)A, AB, BP
59196673986152n-9319(2n-1)2(85n-52)(2n-1)38(152n-93)(85n-52)A, AB, BP
59205911803n-1n3n-1n(3n-1)B=kP
592060885100n-415(5n-1)5(5n-2)(5n-1)5(100n-41)(5n-2)A, AB, BP
592440885108n-493(9n-1)(9n-4)(9n-1)3(108n-49)(9n-4)A, AB, BP
59253653100200n-14125(2n-1)2(61n-43)(2n-1)50(200n-141)(61n-43)A, AB, BP
5930308854n-12n2nn(4n-1)A=B or B=C
6116326159088128n-6716(2n-1)2(342n-179)(2n-1)16(128n-67)(342n-179)A, AB, BP
61163284001696n-358(3n-1)2(129n-47)(3n-1)8(96n-35)(129n-47)A, AB, BP
61163361024848n-354(3n-2)6(11n-8)(3n-2)12(48n-35)(11n-8)A, AB, BP
6116366292823n-82(3n-1)6(23n-8)6(3n-1)(23n-8)B=kP
6116368280624n-112(3n-1)2(9n-4)(3n-1)2(24n-11)(9n-4)A, AB, BP
611648897631n-18n8(31n-1)8n(31n-1)B=kP
611810054900144n-8318(2n-1)4(59n-34)(2n-1)36(144n-83)(59n-34)A, AB, BP
61181225497n-22n2(7n-2)n(7n-2)B=kP
61215610248168n-10721(2n-1)14(11n-7)(2n-1)42(168n-107)(11n-7)A, AB, BP
6123462806184n-12323(2n-1)46(3n-2)(2n-1)46(184n-123)(3n-2)A, AB, BP
61244210248192n-13124(2n-1)6(22n-15)(2n-1)24(192n-131)(22n-15)A, AB, BP
671711401298460136n-6917(2n-1)2(1157n-587)(2n-1)34(136n-69)(1157n-587)A, AB, BP
6717115677452136n-6917(2n-1)34(69n-35)(2n-1)34(136n-69)(69n-35)A, AB, BP
671712062050271n-418n-118(71n-4)18(18n-1)(71n-4)B=kP
6717142856288n-52n-12(5n-3)(2n-1)2(8n-5)(5n-3)A, AB, BP
6717227822784n-1n2n(4n-1)2n(4n-1)A=B or B=C
671824272963108n-419(3n-1)(195n-74)(3n-1)9(108n-41)(195n-74)A, AB, BP
67182433256248n-296(2n-1)(58n-35)(2n-1)6(48n-29)(58n-35)A, AB, BP
6718252562848n-296(2n-1)12(5n-3)(2n-1)12(48n-29)(5n-3)A, AB, BP
6718268241215n-82(2n-1)4(15n-8)4(2n-1)(15n-8)B=kP
6718306113916n-132(2n-1)2(4n-3)(2n-1)(16n-13)(4n-3)A, AB, BP
671840260323n-26n6(23n-2)3n(23n-2)B=kP
6720105562832n-294(2n-1)(10n-9)(2n-1)4(32n-29)(10n-9)A, AB, BP
6721845628168n-10121(2n-1)42(5n-3)(2n-1)42(168n-101)(5n-3)A, AB, BP
6724565628120n-536(5n-1)(25n-11)(5n-1)6(120n-53)(25n-11)A, AB, BP
6728425628224n-15728(2n-1)14(10n-7)(2n-1)28(224n-157)(10n-7)A, AB, BP
67303819095180n-11315(3n-1)(51n-32)(3n-1)15(180n-113)(51n-32)A, AB, BP
67343411394n-12n2nn(4n-1)A=B or B=C
711812791634562144n-7318(2n-1)(2594n-1315)(2n-1)18(144n-73)(2594n-1315)A, AB, BP
71181280817920144n-7318(2n-1)4(649n-329)(2n-1)36(144n-73)(649n-329)A, AB, BP
71181281545706144n-7318(2n-1)3(866n-439)(2n-1)18(144n-73)(866n-439)A, AB, BP
71181282409599108n-379(3n-1)(975n-334)(3n-1)9(108n-37)(975n-334)A, AB, BP
71181284273492144n-7318(2n-1)12(217n-110)(2n-1)36(144n-73)(217n-110)A, AB, BP
7118128718275448n-256(2n-1)(290n-151)(2n-1)6(48n-25)(290n-151)A, AB, BP
71181290137385108n-379(3n-1)3(327n-112)(3n-1)9(108n-37)(327n-112)A, AB, BP
711812969201648n-256(2n-1)4(73n-38)(2n-1)12(48n-25)(73n-38)A, AB, BP
711813056177048n-256(2n-1)3(98n-51)(2n-1)6(48n-25)(98n-51)A, AB, BP
711813144664748n-256(2n-1)2(148n-77)(2n-1)3(48n-25)(148n-77)A, AB, BP
711813323152448n-256(2n-1)12(25n-13)(2n-1)12(48n-25)(25n-13)A, AB, BP
711813492428275n-419n-119(75n-4)19(19n-1)(75n-4)B=kP
711813592144216n-92(2n-1)(34n-19)(2n-1)2(16n-9)(34n-19)A, AB, BP
711813861640148n-256(2n-1)6(52n-27)(2n-1)3(48n-25)(52n-27)A, AB, BP
711814201278079n-82(10n-1)20(79n-8)20(10n-1)(79n-8)B=kP
711814401136016n-92(2n-1)4(9n-5)(2n-1)4(16n-9)(9n-5)A, AB, BP
71181491894683n-123(7n-1)21(83n-12)21(7n-1)(83n-12)B=kP
71181562702987n-162(11n-2)22(87n-16)11(11n-2)(87n-16)B=kP
71181602631916n-92(2n-1)2(20n-11)(2n-1)(16n-9)(20n-11)A, AB, BP
71181704511295n-246(4n-1)24(95n-24)24(4n-1)(95n-24)B=kP
711819173834107n-369(3n-1)27(107n-36)27(3n-1)(107n-36)B=kP
711821303195119n-486(5n-2)30(119n-48)15(5n-2)(119n-48)B=kP
7118255625564n-1n2n(4n-1)2n(4n-1)A=B or B=C
7119270364230152n-8119(2n-1)2(289n-154)(2n-1)38(152n-81)(289n-154)A, AB, BP
7119284539615n-44n-14(15n-4)4(4n-1)(15n-4)B=kP
7119342127816n-94n-12(2n-1)(4n-1)2(16n-9)(2n-1)A, AB, BP
7120158112180160n-8920(2n-1)2(178n-99)(2n-1)20(160n-89)(178n-99)A, AB, BP
712016011360120n-4910(3n-1)5(27n-11)(3n-1)10(120n-49)(27n-11)A, AB, BP
7120180127832n-254(2n-1)4(4n-3)(2n-1)2(32n-25)(4n-3)A, AB, BP
712028435515n-44n4(15n-4)n(15n-4)B=kP
7121126127848n-253(4n-1)6(2n-1)(4n-1)6(48n-25)(2n-1)A, AB, BP
71229271852176n-10522(2n-1)4(57n-34)(2n-1)44(176n-105)(57n-34)A, AB, BP
712299127832n-252(4n-1)(4n-3)(4n-1)2(32n-25)(4n-3)A, AB, BP
71247117043n-1n3n-1n(3n-1)B=kP
7124721278120n-496(5n-1)6(5n-2)(5n-1)6(120n-49)(5n-2)A, AB, BP
71265651688208n-13726(2n-1)4(41n-27)(2n-1)52(208n-137)(41n-27)A, AB, BP
712754127860n-493(5n-1)(5n-4)(5n-1)3(60n-49)(5n-4)A, AB, BP
7130451278144n-736(6n-1)9(2n-1)(6n-1)18(144n-73)(2n-1)A, AB, BP
71324011360192n-12116(3n-1)2(27n-17)(3n-1)16(192n-121)(27n-17)A, AB, BP
71363612784n-12n2nn(4n-1)A=B or B=C
732021030660160n-8720(2n-1)10(46n-25)(2n-1)20(160n-87)(46n-25)A, AB, BP
7320219438011n-43n-13(11n-4)3(3n-1)(11n-4)B=kP
7320220401560n-475(3n-2)5(9n-7)(3n-2)5(60n-47)(9n-7)A, AB, BP
732029273015n-24n4(15n-2)2n(15n-2)B=kP
732114030660168n-9521(2n-1)14(23n-13)(2n-1)42(168n-95)(23n-13)A, AB, BP
732114630667n-42n-12(7n-4)2(2n-1)(7n-4)B=kP
73221104015132n-5911(3n-1)11(9n-4)(3n-1)11(132n-59)(9n-4)A, AB, BP
792015812497980240n-16120(3n-2)3(1601n-1074)(3n-2)60(240n-161)(1601n-1074)A, AB, BP
792015821249780160n-8120(2n-1)2(1602n-811)(2n-1)20(160n-81)(1602n-811)A, AB, BP
79201584625680120n-4110(3n-1)3(401n-137)(3n-1)30(120n-41)(401n-137)A, AB, BP
79201585500860160n-8120(2n-1)5(642n-325)(2n-1)20(160n-81)(642n-325)A, AB, BP
79201588313630120n-4110(3n-1)2(603n-206)(3n-1)10(120n-41)(603n-206)A, AB, BP
79201590251220160n-8120(2n-1)10(322n-163)(2n-1)20(160n-81)(322n-163)A, AB, BP
7920159615760560n-415(3n-2)3(101n-69)(3n-2)15(60n-41)(101n-69)A, AB, BP
79201600126400120n-4110(3n-1)5(243n-83)(3n-1)10(120n-41)(243n-83)A, AB, BP
7920160510143632n-174(2n-1)(130n-69)(2n-1)4(32n-17)(130n-69)A, AB, BP
7920162063990120n-4110(3n-1)30(41n-14)(3n-1)30(120n-41)(41n-14)A, AB, BP
792016305150832n-174(2n-1)2(66n-35)(2n-1)4(32n-17)(66n-35)A, AB, BP
792016593318083n-421n-121(83n-4)21(21n-1)(83n-4)B=kP
792016603278560n-415(3n-2)5(63n-43)(3n-2)5(60n-41)(63n-43)A, AB, BP
792016802654424n-172(3n-2)3(17n-12)(3n-2)6(24n-17)(17n-12)A, AB, BP
792017381738087n-82(11n-1)22(87n-8)22(11n-1)(87n-8)B=kP
792017801406224n-172(3n-2)2(27n-19)(3n-2)2(24n-17)(27n-19)A, AB, BP
79201896948095n-164(6n-1)24(95n-16)24(6n-1)(95n-16)B=kP
79201975790099n-205(5n-1)25(99n-20)25(5n-1)(99n-20)B=kP
79201980782112n-53n-13(5n-2)(3n-1)3(12n-5)(5n-2)A, AB, BP
792022125530111n-324(7n-2)28(111n-32)14(7n-2)(111n-32)B=kP
792023704740119n-4010(3n-1)30(119n-40)30(3n-1)(119n-40)B=kP
792028443555143n-644(9n-4)36(143n-64)9(9n-4)(143n-64)B=kP
7920316031604n-1n2n(4n-1)2n(4n-1)A=B or B=C
7921332550788168n-8921(2n-1)2(353n-187)(2n-1)42(168n-89)(353n-187)A, AB, BP
792133626544168n-8921(2n-1)42(17n-9)(2n-1)42(168n-89)(17n-9)A, AB, BP
7921420158024n-173(2n-1)6(3n-2)(2n-1)2(24n-17)(3n-2)A, AB, BP
7921474110623n-133(2n-1)6(23n-13)2(2n-1)(23n-13)B=kP
79221987821132n-5311(3n-1)33(5n-2)(3n-1)33(132n-53)(5n-2)A, AB, BP
7922220158024n-172(3n-1)2(3n-2)(3n-1)2(24n-17)(3n-2)A, AB, BP
792411226544144n-6512(3n-1)2(51n-23)(3n-1)12(144n-65)(51n-23)A, AB, BP
7924120158056n-332(7n-2)(7n-4)(7n-2)2(56n-33)(7n-4)A, AB, BP
7925100158060n-415(3n-1)5(3n-2)(3n-1)5(60n-41)(3n-2)A, AB, BP
792870158064n-494(4n-1)2(4n-3)(4n-1)4(64n-49)(4n-3)A, AB, BP
7930601580160n-8110(4n-1)20(2n-1)(4n-1)20(160n-81)(2n-1)A, AB, BP
7936447821180n-1019(5n-1)(25n-14)(5n-1)9(180n-101)(25n-14)A, AB, BP
7936451580160n-814(10n-1)5(2n-1)(10n-1)20(160n-81)(2n-1)A, AB, BP
79404015804n-12n2nn(4n-1)A=B or B=C
832117443039792168n-8521(2n-1)2(1765n-893)(2n-1)42(168n-85)(1765n-893)A, AB, BP
832117461014426168n-8521(2n-1)6(589n-298)(2n-1)42(168n-85)(589n-298)A, AB, BP
83211750435750168n-8521(2n-1)14(253n-128)(2n-1)42(168n-85)(253n-128)A, AB, BP
8321175233930456n-297(2n-1)2(197n-102)(2n-1)14(56n-29)(197n-102)A, AB, BP
83211764146412168n-8521(2n-1)42(85n-43)(2n-1)42(168n-85)(85n-43)A, AB, BP
832117926374424n-133(2n-1)2(37n-20)(2n-1)6(24n-13)(37n-20)A, AB, BP
832118064996656n-297(2n-1)14(29n-15)(2n-1)14(56n-29)(29n-15)A, AB, BP
832118263834687n-422n-122(87n-4)22(22n-1)(87n-4)B=kP
832118902241024n-133(2n-1)6(13n-7)(2n-1)6(24n-13)(13n-7)A, AB, BP
832119921394495n-123(8n-1)24(95n-12)24(8n-1)(95n-12)B=kP
8321218486328n-52n-12(5n-3)(2n-1)2(8n-5)(5n-3)A, AB, BP
832123246972111n-287(4n-1)28(111n-28)28(4n-1)(111n-28)B=kP
832124905810119n-363(10n-3)30(119n-36)10(10n-3)(119n-36)B=kP
8321348634864n-1n2n(4n-1)2n(4n-1)A=B or B=C
8322366167079132n-4911(3n-1)3(97n-36)(3n-1)33(132n-49)(97n-36)A, AB, BP
832237415521132n-4911(3n-1)11(27n-10)(3n-1)11(132n-49)(27n-10)A, AB, BP
8322462174316n-132(2n-1)2(4n-3)(2n-1)(16n-13)(4n-3)A, AB, BP
8324156863264n-458(2n-1)4(10n-7)(2n-1)8(64n-45)(10n-7)A, AB, BP
832416619927n-12n2(7n-1)2n(7n-1)B=kP
8324168174336n-253(3n-1)3(3n-2)(3n-1)3(36n-25)(3n-2)A, AB, BP
83261048632208n-12526(2n-1)52(5n-3)(2n-1)52(208n-125)(5n-3)A, AB, BP
8327902241072n-619(2n-1)2(13n-11)(2n-1)18(72n-61)(13n-11)A, AB, BP
83288323243n-1n3n-1n(3n-1)B=kP
8328841743140n-577(5n-1)7(5n-2)(5n-1)7(140n-57)(5n-2)A, AB, BP
833070174372n-616(3n-1)2(6n-5)(3n-1)3(72n-61)(6n-5)A, AB, BP
833649146412288n-20536(2n-1)(170n-121)(2n-1)36(288n-205)(170n-121)A, AB, BP
83424217434n-12n2nn(4n-1)A=B or B=C
892369061410184n-9523(2n-1)46(31n-16)(2n-1)46(184n-95)(31n-16)A, AB, BP
89237121637631n-48n-18(31n-4)8(8n-1)(31n-4)B=kP
8924306108936192n-10324(2n-1)6(110n-59)(2n-1)24(192n-103)(110n-59)A, AB, BP
89243121388472n-556(3n-2)3(21n-16)(3n-2)6(72n-55)(21n-16)A, AB, BP
8924356213615n-14n4(15n-1)4n(15n-1)B=kP
892453471223n-36n6(23n-3)2n(23n-3)B=kP
892615613884208n-11926(2n-1)52(7n-4)(2n-1)52(208n-119)(7n-4)A, AB, BP
892617811577n-22n2(7n-2)n(7n-2)B=kP
89308926703n-1n3n-1n(3n-1)B=kP
89395213884312n-22339(2n-1)26(7n-5)(2n-1)78(312n-223)(7n-5)A, AB, BP
9725810392850200n-10325(2n-1)10(167n-86)(2n-1)50(200n-103)(167n-86)A, AB, BP
97258501649040n-235(2n-1)10(7n-4)(2n-1)10(40n-23)(7n-4)A, AB, BP
9725970485039n-205(2n-1)10(39n-20)10(2n-1)(39n-20)B=kP
972636435308208n-11126(2n-1)52(15n-8)(2n-1)52(208n-111)(15n-8)A, AB, BP
9726388504415n-82(2n-1)4(15n-8)4(2n-1)(15n-8)B=kP
972818235308224n-12728(2n-1)14(30n-17)(2n-1)28(224n-127)(30n-17)A, AB, BP
972819427167n-12n2(7n-1)2n(7n-1)B=kP
97348516490272n-17534(2n-1)17(14n-9)(2n-1)34(272n-175)(14n-9)A, AB, BP

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