## 11．解と恒等式の一覧表

### 4/p＝1/a＋1/b＋1/c, final (2〜47)

pabc PABC type
21223n-1n3n-1n(3n-1)B=kP
314128n-52n-12(5n-3)(2n-1)2(8n-5)(5n-3)A, AB, BP
31664n-1n2n(4n-1)2n(4n-1)A=B or B=C
32234n-12n2nn(4n-1)A=B or B=C
5242016n-112(2n-1)4(3n-2)(2n-1)4(16n-11)(3n-2)A, AB, BP
525103n-1n3n-1n(3n-1)B=kP
721521016n-92(2n-1)(34n-19)(2n-1)2(16n-9)(34n-19)A, AB, BP
721611216n-92(2n-1)4(9n-5)(2n-1)4(16n-9)(9n-5)A, AB, BP
72186312n-53n-13(5n-2)(3n-1)3(12n-5)(5n-2)A, AB, BP
72214211n-43n-13(11n-4)3(3n-1)(11n-4)B=kP
7228284n-1n2n(4n-1)2n(4n-1)A=B or B=C
7361416n-94n-12(2n-1)(4n-1)2(16n-9)(2n-1)A, AB, BP
744144n-12n2nn(4n-1)A=B or B=C
11334112224n-133(2n-1)2(37n-20)(2n-1)6(24n-13)(37n-20)A, AB, BP
1133639624n-133(2n-1)6(13n-7)(2n-1)6(24n-13)(13n-7)A, AB, BP
113421548n-52n-12(5n-3)(2n-1)2(8n-5)(5n-3)A, AB, BP
1134413215n-44n-14(15n-4)4(4n-1)(15n-4)B=kP
11366664n-1n2n(4n-1)2n(4n-1)A=B or B=C
114939632n-214(2n-1)(26n-17)(2n-1)4(32n-21)(26n-17)A, AB, BP
11411443n-1n3n-1n(3n-1)B=kP
114123320n-95n-1(5n-2)(5n-1)(20n-9)(5n-2)A, AB, BP
1166334n-12n2nn(4n-1)A=B or B=C
1341846832n-194(2n-1)2(22n-13)(2n-1)4(32n-19)(22n-13)A, AB, BP
1342013024n-112(3n-1)2(9n-4)(3n-1)2(24n-11)(9n-4)A, AB, BP
13426527n-12n2(7n-1)2n(7n-1)B=kP
1351013040n-275(2n-1)10(3n-2)(2n-1)10(40n-27)(3n-2)A, AB, BP
1753051040n-235(2n-1)10(7n-4)(2n-1)10(40n-23)(7n-4)A, AB, BP
175341707n-42n-12(7n-4)2(2n-1)(7n-4)B=kP
1761551048n-316(2n-1)3(14n-9)(2n-1)6(48n-31)(14n-9)A, AB, BP
176171023n-1n3n-1n(3n-1)B=kP
19596912040n-215(2n-1)2(101n-53)(2n-1)10(40n-21)(101n-53)A, AB, BP
195100190040n-215(2n-1)10(21n-11)(2n-1)10(40n-21)(21n-11)A, AB, BP
19511457023n-46n-16(23n-4)6(6n-1)(23n-4)B=kP
1951204568n-52n-12(5n-3)(2n-1)2(8n-5)(5n-3)A, AB, BP
1951901904n-1n2n(4n-1)2n(4n-1)A=B or B=C
19623262248n-296(2n-1)(58n-35)(2n-1)6(48n-29)(58n-35)A, AB, BP
1962445648n-296(2n-1)12(5n-3)(2n-1)12(48n-29)(5n-3)A, AB, BP
196309516n-132(2n-1)2(4n-3)(2n-1)(16n-13)(4n-3)A, AB, BP
19638577n-22n2(7n-2)n(7n-2)B=kP
1981245648n-294(3n-1)3(5n-3)(3n-1)12(48n-29)(5n-3)A, AB, BP
191010954n-12n2nn(4n-1)A=B or B=C
2361391918248n-256(2n-1)(290n-151)(2n-1)6(48n-25)(290n-151)A, AB, BP
236140966048n-256(2n-1)4(73n-38)(2n-1)12(48n-25)(73n-38)A, AB, BP
236141648648n-256(2n-1)3(98n-51)(2n-1)6(48n-25)(98n-51)A, AB, BP
236142489936n-133(3n-1)(111n-40)(3n-1)3(36n-13)(111n-40)A, AB, BP
236144331248n-256(2n-1)12(25n-13)(2n-1)12(48n-25)(25n-13)A, AB, BP
236147225416n-92(2n-1)(34n-19)(2n-1)2(16n-9)(34n-19)A, AB, BP
236150172536n-133(3n-1)3(39n-14)(3n-1)3(36n-13)(39n-14)A, AB, BP
236156119616n-92(2n-1)4(9n-5)(2n-1)4(16n-9)(9n-5)A, AB, BP
23616196627n-47n-17(27n-4)7(7n-1)(27n-4)B=kP
23617466716n-92(2n-1)2(20n-11)(2n-1)(16n-9)(20n-11)A, AB, BP
23618455231n-82(4n-1)8(31n-8)8(4n-1)(31n-8)B=kP
23620741435n-123(3n-1)9(35n-12)9(3n-1)(35n-12)B=kP
23623034539n-162(5n-2)10(39n-16)5(5n-2)(39n-16)B=kP
2362762764n-1n2n(4n-1)2n(4n-1)A=B or B=C
2374213816n-94n-12(2n-1)(4n-1)2(16n-9)(2n-1)A, AB, BP
238231843n-1n3n-1n(3n-1)B=kP
2382413840n-172(5n-1)2(5n-2)(5n-1)2(40n-17)(5n-2)A, AB, BP
23916331272n-499(2n-1)2(25n-17)(2n-1)18(72n-49)(25n-17)A, AB, BP
2391813848n-253(4n-1)6(2n-1)(4n-1)6(48n-25)(2n-1)A, AB, BP
23101513848n-252(6n-1)3(2n-1)(6n-1)6(48n-25)(2n-1)A, AB, BP
2312121384n-12n2nn(4n-1)A=B or B=C
29878904864n-358(2n-1)2(86n-47)(2n-1)8(64n-35)(86n-47)A, AB, BP
29880232048n-194(3n-1)2(33n-13)(3n-1)4(48n-19)(33n-13)A, AB, BP
2988769611n-43n-13(11n-4)3(3n-1)(11n-4)B=kP
2988863824n-192(3n-2)2(9n-7)(3n-2)2(24n-19)(9n-7)A, AB, BP
29811623215n-14n4(15n-1)4n(15n-1)B=kP
2910292903n-1n3n-1n(3n-1)B=kP
29112263888n-5911(2n-1)22(3n-2)(2n-1)22(88n-59)(3n-2)A, AB, BP
3182496175264n-338(2n-1)(514n-265)(2n-1)8(64n-33)(514n-265)A, AB, BP
3182503100064n-338(2n-1)2(258n-133)(2n-1)8(64n-33)(258n-133)A, AB, BP
3182521562448n-174(3n-1)3(65n-23)(3n-1)12(48n-17)(65n-23)A, AB, BP
318256793648n-174(3n-1)2(99n-35)(3n-1)4(48n-17)(99n-35)A, AB, BP
318264409224n-172(3n-2)3(17n-12)(3n-2)6(24n-17)(17n-12)A, AB, BP
318279223235n-49n-19(35n-4)9(9n-1)(35n-4)B=kP
318280217024n-172(3n-2)2(27n-19)(3n-2)2(24n-17)(27n-19)A, AB, BP
318310124039n-82(5n-1)10(39n-8)10(5n-1)(39n-8)B=kP
318312120912n-53n-13(5n-2)(3n-1)3(12n-5)(5n-2)A, AB, BP
31837274447n-164(3n-1)12(47n-16)12(3n-1)(47n-16)B=kP
3184964964n-1n2n(4n-1)2n(4n-1)A=B or B=C
319561562472n-419(2n-1)2(65n-37)(2n-1)18(72n-41)(65n-37)A, AB, BP
319625587n-42n-12(7n-4)2(2n-1)(7n-4)B=kP
3197224820n-95n-1(5n-2)(5n-1)(20n-9)(5n-2)A, AB, BP
311035217080n-4910(2n-1)5(18n-11)(2n-1)10(80n-49)(18n-11)A, AB, BP
31104024824n-172(3n-1)2(3n-2)(3n-1)2(24n-17)(3n-2)A, AB, BP
311222409296n-6512(2n-1)2(34n-23)(2n-1)12(96n-65)(34n-23)A, AB, BP
31122424856n-252(7n-1)(7n-3)(7n-1)2(56n-25)(7n-3)A, AB, BP
3116162484n-12n2nn(4n-1)A=B or B=C
37101242294080n-4310(2n-1)4(67n-36)(2n-1)20(80n-43)(67n-36)A, AB, BP
3710125925080n-4310(2n-1)5(54n-29)(2n-1)10(80n-43)(54n-29)A, AB, BP
3710130240560n-235(3n-1)5(21n-8)(3n-1)5(60n-23)(21n-8)A, AB, BP
3710140103616n-112(2n-1)4(3n-2)(2n-1)4(16n-11)(3n-2)A, AB, BP
371014874015n-82(2n-1)4(15n-8)4(2n-1)(15n-8)B=kP
371018537019n-15n5(19n-1)5n(19n-1)B=kP
371242103632n-274(2n-1)2(6n-5)(2n-1)4(32n-27)(6n-5)A, AB, BP
3714281036112n-7514(2n-1)28(3n-2)(2n-1)28(112n-75)(3n-2)A, AB, BP
3716226512128n-9116(2n-1)2(38n-27)(2n-1)16(128n-91)(38n-27)A, AB, BP
4111154631488n-4711(2n-1)22(15n-8)(2n-1)22(88n-47)(15n-8)A, AB, BP
4111164180415n-44n-14(15n-4)4(4n-1)(15n-4)B=kP
411272295272n-316(3n-1)9(7n-3)(3n-1)18(72n-31)(7n-3)A, AB, BP
4112824927n-12n2(7n-1)2n(7n-1)B=kP
411212316411n-33n3(11n-3)n(11n-3)B=kP
4114415743n-1n3n-1n(3n-1)B=kP
4118242952144n-10318(2n-1)12(7n-5)(2n-1)36(144n-103)(7n-5)A, AB, BP
431147422420288n-4511(2n-1)2(485n-248)(2n-1)22(88n-45)(485n-248)A, AB, BP
43114842081288n-4511(2n-1)22(45n-23)(2n-1)22(88n-45)(45n-23)A, AB, BP
4311516567647n-412n-112(47n-4)12(12n-1)(47n-4)B=kP
431159423228n-52n-12(5n-3)(2n-1)2(8n-5)(5n-3)A, AB, BP
43119469464n-1n2n(4n-1)2n(4n-1)A=B or B=C
43121041341672n-296(3n-1)(87n-35)(3n-1)6(72n-29)(87n-35)A, AB, BP
4312105602032n-214(2n-1)(26n-17)(2n-1)4(32n-21)(26n-17)A, AB, BP
4312108232272n-296(3n-1)18(5n-2)(3n-1)18(72n-29)(5n-2)A, AB, BP
431212951611n-13n3(11n-1)3n(11n-1)B=kP
431213247320n-175n-3(5n-4)(5n-3)(20n-17)(5n-4)A, AB, BP
431217225815n-24n4(15n-2)2n(15n-2)B=kP
43153824510120n-7715(2n-1)2(53n-34)(2n-1)30(120n-77)(53n-34)A, AB, BP
431827232296n-536(4n-1)(20n-11)(4n-1)6(96n-53)(20n-11)A, AB, BP
4322224734n-12n2nn(4n-1)A=B or B=C
471256531866096n-4912(2n-1)(1154n-589)(2n-1)12(96n-49)(1154n-589)A, AB, BP
471256615961296n-4912(2n-1)2(578n-295)(2n-1)12(96n-49)(578n-295)A, AB, BP
471256710659696n-4912(2n-1)3(386n-197)(2n-1)12(96n-49)(386n-197)A, AB, BP
47125688008872n-256(3n-1)(435n-151)(3n-1)6(72n-25)(435n-151)A, AB, BP
47125705358096n-4912(2n-1)6(194n-99)(2n-1)12(96n-49)(194n-99)A, AB, BP
47125724032672n-256(3n-1)2(219n-76)(3n-1)6(72n-25)(219n-76)A, AB, BP
47125733590832n-174(2n-1)(130n-69)(2n-1)4(32n-17)(130n-69)A, AB, BP
47125762707272n-256(3n-1)9(49n-17)(3n-1)18(72n-25)(49n-17)A, AB, BP
47125802044536n-253(3n-2)(111n-77)(3n-2)3(36n-25)(111n-77)A, AB, BP
47125821823632n-174(2n-1)2(66n-35)(2n-1)4(32n-17)(66n-35)A, AB, BP
47125881381872n-256(3n-1)6(75n-26)(3n-1)6(72n-25)(75n-26)A, AB, BP
4712600940032n-174(2n-1)8(17n-9)(2n-1)8(32n-17)(17n-9)A, AB, BP
4712611733251n-413n-113(51n-4)13(13n-1)(51n-4)B=kP
4712612719136n-253(3n-2)9(13n-9)(3n-2)9(36n-25)(13n-9)A, AB, BP
4712636498232n-174(2n-1)4(36n-19)(2n-1)2(32n-17)(36n-19)A, AB, BP
4712658394855n-82(7n-1)14(55n-8)14(7n-1)(55n-8)B=kP
4712705282059n-123(5n-1)15(59n-12)15(5n-1)(59n-12)B=kP
4712708277320n-135n-3(25n-16)(5n-3)(20n-13)(25n-16)A, AB, BP
4712752225663n-164(4n-1)16(63n-16)16(4n-1)(63n-16)B=kP
4712846169271n-246(3n-1)18(71n-24)18(3n-1)(71n-24)B=kP
4712940141079n-324(5n-2)20(79n-32)10(5n-2)(79n-32)B=kP
4712987131683n-363(7n-3)21(83n-36)7(7n-3)(83n-36)B=kP
4712112811284n-1n2n(4n-1)2n(4n-1)A=B or B=C
471315656420n-135n-2(5n-3)(5n-2)(20n-13)(5n-3)A, AB, BP
47148456432n-172(4n-1)4(2n-1)(4n-1)4(32n-17)(2n-1)A, AB, BP
4714943297n-22n2(7n-2)n(7n-2)B=kP
47156056436n-253(3n-1)3(3n-2)(3n-1)3(36n-25)(3n-2)A, AB, BP
4716477523n-1n3n-1n(3n-1)B=kP
47164856440n-332(5n-2)(5n-4)(5n-2)2(40n-33)(5n-4)A, AB, BP
4718347191108n-619(3n-1)(39n-22)(3n-1)9(108n-61)(39n-22)A, AB, BP
47183656496n-496(4n-1)12(2n-1)(4n-1)12(96n-49)(2n-1)A, AB, BP
47203056496n-494(6n-1)6(2n-1)(6n-1)12(96n-49)(2n-1)A, AB, BP
47212856496n-493(8n-1)4(2n-1)(8n-1)12(96n-49)(2n-1)A, AB, BP
4724245644n-12n2nn(4n-1)A=B or B=C

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