 Computational Number Theory

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このホームページではコンピュータによる数論を紹介します Update 2021.4.2

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```             [466. x^6 + ky^3 = z^6 + kw^3(2021.4.2)]
[465. x^m + ky^3 = z^m + kw^3(2021.4.1)]
[464. x^3 + y^3 = p(2021.3.26)]
[463. Index of Generalized Taxicab Number(2021.3.22)]
[462. x^3 + y^3 + z^3 - 3xyz = 1 Ⅱ(2021.3.12)]
[461. x^3 + y^3 + z^3 - 3xyz = 1 Ⅰ(2021.3.10)]
[460. x^3 + y^3 + z^3 = 3xyz(2021.3.8)]
[459. ax^3 + by^3 + cz^3 = dxyz Ⅲ(2021.3.6)]
[458. ax^3 + by^3 + cz^3 = dxyz Ⅱ(2021.3.5)]
[457. ax^3 + by^3 + cz^3 = dxyz Ⅰ(2021.3.2)]
[456. x^3+y^3+z^3=nxyz(2021.2.25)]
[455. Index of ax^6 + by^6 + cz^6 = w^2(2021.2.23)]
[454. 48x^6 + 24y^6 - 72z^6 = w^2(2021.2.22)]
[453. 48x^6 + 12y^6 - 60z^6 = w^2(2021.2.20)]
[452. 46x^6 + 12y^6 - 58z^6 = w^2(2021.2.19)]
[451. 45x^6 + 20y^6 - 65z^6 = w^2(2021.2.18)]
[450. 42x^6 + 28y^6 - 70z^6 = w^2(2021.2.16)]
[449. ax^6 + by^6 + cz^6 = w^2 Ⅳ(2021.2.15)]
[448. ax^6 + by^6 + cz^6 = w^2 Ⅲ(2021.2.15)]
[447. 40x^6 + 24y^6 - 64z^6 = w^2(2021.2.14)]
[446. 40x^6 + 8y^6 - 48z^6  = w^2(2021.2.13)]
[445. ax^6 + by^6 + cz^6 = w^2 Ⅵ(2021.2.13)]
[444. 39x^6 + 36y^6 - 75z^6 = w^2(2021.2.10)]
[443. 39x^6 + 13y^6 - 52z^6 = w^2(2021.2.9)]
[442. 38x^6 + 20y^6 - 58z^6 = w^2(2021.2.7)]
[441. 38x^6 + 10y^6 - 48z^6 = w^2(2021.2.5)]
[440. 36x^6 + 12y^6 - 48z^6 = w^2(2021.2.4)]
[439. 33x^6 + 3y^6 - 36z^6  = w^2(2021.2.3)]
[438. 30x^6 + 20y^6 - 50z^6 = w^2(2021.2.2)]
[437. 30x^6 + 6y^6 - 36z^6  = w^2(2021.1.31)]
[436. 28x^6 + 14y^6 - 42z^6 = w^2(2021.1.29)]
[435. 27x^6 + 12y^6 - 39z^6 = w^2(2021.1.28)]
[434. 25x^6 + 20y^6 - 45z^6 = w^2(2021.1.26)]
[433. 24x^6 + 16y^6 - 40z^6 = w^2(2021.1.25)]
[432. 21x^6 + 7y^6 - 28z^6  = w^2(2021.1.22)]
[431. 20x^6 + 10y^6 - 30z^6 = w^2(2021.1.21)]
[430. 20x^6 + 5y^6 - 25z^6  = w^2(2021.1.20)]
[429. 16x^6 + 9y^6 - 25z^6  = w^2(2021.1.18)]
[428. 16x^6 + 2y^6 - 18z^6  = w^2(2021.1.17)]
[427. 15x^6 + 5y^6 - 20z^6  = w^2(2021.1.14)]
[426. 12x^6 + 6y^6 - 18z^6  = w^2(2021.1.12)]
[425. 12x^6 + 3y^6 - 15z^6  = w^2(2021.1.11)]
[424. 10x^6 + 6y^6 - 16z^6  = w^2(2021.1.10)]
[423. 10x^6 + 2y^6 - 12z^6  = w^2(2021.1.9)]
[422. 9x^6 + 3y^6 - 12z^6   = w^2(2021.1.7)]
[421. 6x^6 + 4y^6 - 10z^6 = w^2(2021.1.6)]
[420. ax^6 + by^6 + cz^6 = w^2 Ⅴ(2021.1.5)]
[419. -27x^6 - y^6 + z^6 = w^2(2021.1.4)]
[418. -12x^6 + 6y^6 - 48z^6 = w^2(2021.1.4)]
[417. -48x^6 + 6y^6 - 6z^6 = w^2(2021.1.4)]
[416. -12x^6 + 6y^6 - 6z^6 = w^2(2021.1.2)]
[415. Sum of consecutive squares equal to a a 4th power(2020.12.14)]
[414. Sum of consecutive squares equal to a cube(2020.12.9)]
[413. Sum of consecutive squares equal to a square(2020.12.6)]
[412. Sum of consecutive cubes equal to a cube(2020.12.2)]
[411. Sum of consecutive cubes equal to a perfect square(2020.11.29)]
[410. x^4 + y^4 + k = z^2(2020.11.18)]
[409. Parametric solution of (x1^3 + x2^3 )(y1^3 + y2^3 ) = z1^3 + z2^3 Ⅱ(2020.11.10)]
[408. Parametric solution of (x1^3 + x2^3 )(y1^3 + y2^3 ) = z1^3 + z2^3 Ⅰ(2020.10.23)]
[407. Parametric solution of ax^n + by^n + cz^n + dw^n = 0 (2020.10.16)]
[406. Table of solutions for ax^3 + ay^3 + cz^3 + dw^3 = 0 (2020.10.3)]
[405. Parametric solutions of ax^3 + by^3 + cz^3 + dw^3 = 0 Ⅲ  (2020.9.28)]
[404. Parametric solutions of ax^3 + by^3 + cz^3 + dw^3 = 0 Ⅱ  (2020.9.22)(2020.10.15)]
[403. Table of solutions for ax^3 + by^3 = cz^3 + dw^3  (2020.9.14)]
[402. Solutions  of  x^4 + y^4 + z^4 = nw^2  (2010.9.1)(2020.9.6)]
[401. 1/n=1/x1^2+1/x2^2+...1/xk^2(2020.6.26)(2020.7.3)]
[400. a^2X^6 + b^2Y^6 + 2abZ^3 = W^6(2020.6.14)]
[399. ax^4 + by^4 + cz^4 + dw^4 + eu^4= 0 Ⅱ(2020.6.6)]
[398. Table of solutions for ax^4 + by^4 + cz^4 + dw^4 = 0 (2020.5.28)]
[397. Index of ax^4 + by^4 + cz^4 + dw^4 = 0, abcd=□ (2020.5.11)]
[396. 4(m^2-1)X^4 + (1-m^2)(m^2+3)Y^4 = -(m^2-1)^2Z^4 + 4(m^2+3)W^4 (2020.5.11)]
[395. (d^2-2dm^2+2m^4)X^4 + (d^2-2dm^2+2m^4)Y^4 = 2(-d+m^2)^2Z^4 + 2W^4 (2020.5.10)]
[394. -dm^2(d+2)X^4 + (-2m^2+d+2)m^2(d-2m^2)Y^4 = d(d-2m^2)m^4Z^4 + (d+2)(2m^2-d-2)W^4 (2020.5.9)]
[393. (m^4+1)X^4 + (m^4+1)Y^4 = 2Z^4 + 2W^4 (2020.5.7)]
[392. 2mnX^4 + (m^2-n^2)Y^4 = 2mnZ^4 + (m^2-n^2)W^4 (2020.5.4)]
[391. Index of ax^4 + by^4 + cz^4 + dw^4 = 0, abcd≠□ (2020.4.27)]
[390. (m^2+1)^2(m^2-1)X^4 + (m^2-1)Y^4 + (m^2+1)Z^4 = 2m^2W^4 (2020.4.26)]
[389. (d-2)(d+2)^2X^4 + (4d-8)Y^4 + Z^4 = (4d+8)W^4 (2020.4.25)]
[388. pr^2X^4 + 4p(p+r)^2Y^4 + r^3Z^4 = r^2(p+r)W^4 (2020.4.24)]
[387. 5X^4 + 45Y^4 + Z^4 = 6W^4 (2020.4.23)]
[386. 2X^4 + 8Y^4 + Z^4 = 9W^4 (2020.4.22)]
[385. 31X^4 + 31Y^4 + Z^4 = 2W^4 (2020.4.21)]
[384. 7X^4 + 7Y^4 + 2Z^4 = 9W^4 (2020.4.20)]
[383. 25X^4 + 4Y^4 + Z^4 = 5W^4 (2020.4.19)]
[382. 79X^4 + 79Y^4 + 4Z^4 = 2W^4 (2020.4.18)]
[381. 57X^4 + 57Y^4 = 8Z^4 + W^4(2020.4.16)]
[380. 18X^4 + 8Y^4 + Z^4 = 27W^4(2020.4.15)]
[379. 73X^4 + 73Y^4 + Z^4 = 2W^4(2020.4.14)]
[378. 75X^4 + 3Y^4 + 2Z^4 = 5W^4(2020.4.13)]
[377. pX^4 + pY^4 = 2Z^4 + W^4 revisited(2020.4.12)]
[376. 33X^4 + 33Y^4 = 2Z^4 + W^4(2020.4.9)]
[375. 3X^4 + 3Y^4 = 2Z^4 + W^4(2020.4.8)]
[374. 9X^4 + 4Y^4 + 2Z^4 = 6W^4(2020.4.6)]
[373. d^2a^2X^4 + (-d+2a)^2a^2Y^4 + 2d(-d+2a)Z^4 = 4a^2W^4(2020.4.4)]
[372. 25X^4 + 25Y^4 + 8Z^4 = 25W^4(2020.4.4)]
[371. X^4 + 9Y^4 + 6Z^4 = W^4(2020.4.4)]
[370. 9X^4 + 36Y^4 + 4Z^4 = 9W^4(2020.4.4)]
[369. pX^4 + pY^4 + 2Z^4 = sW^4(2020.4.2)]
[368. 7X^4 + 7Y^4 + Z^4 = 8W^4(2020.4.2)]
[367. 47X^4 + 47Y^4 + 2Z^4 = 49W^4(2020.4.1)]
[366. 23X^4 + 23Y^4 + 2Z^4 = 25W^4(2020.3.31)]
[365. pX^4 + pY^4 = 2Z^4 + W^4(2020.3.28)]
[364. X^4 + 36Y^4 + 27Z^4 = 4W^4(2020.3.27)]
[363. 49X^4 + 49Y^4 + 8Z^4 = W^4(2020.3.26)]
[362. 3X^4 + 75Y^4 + 5Z^4 = 8W^4(2020.3.25)]
[361. 36X^4 + Y^4 + 3Z^4 = W^4(2020.3.23)]
[360. 165 = (-385495523231271884)^3 + 383344975542639445^3 + 98422560467622814^3  (2020.3.19)]
[359. 25X^4 + Y^4 + 10Z^4 = W^4(2020.3.18)]
[358. 50X^4 + 2Y^4 + 5Z^4 = 2W^4(2020.3.16)]
[357. 27X^4 + 12Y^4 = 4Z^4 + 3W^4(2020.3.14)]
[356. 4X^4 + Y^4 + Z^4 = W^4(2020.3.12)]
[355. 31X^4 + 31Y^4 + 2Z^4 = W^4(2020.3.10)]
[354. 12X^4 + 12Y^4 = 8Z^4 + W^4(2020.3.9)]
[353. 19X^4 + 19Y^4 = 2Z^4 + W^4(2020.3.8)]
[352. 17X^4 + 17Y^4 = 18Z^4 + W^4(2020.3.7)]
[351. 9X^4 + Y^4 + 2Z^4 = 3W^4(2020.3.6)]
[350. 12X^4 + 3Y^4 + Z^4 = W^4(2020.3.4)]
[349. 9X^4 + 4Y^4 + 3Z^4 = W^4(2020.3.2)]
[348. 9X^4 + 9Y^4 = 2Z^4 + W^4(2020.3.1)]
[347. New solution: 4108 = 10378929361429825^3 + (-10007234208296573)^3 + 2*(-3869419050286010)^3(2020.2.22)]
[346. New solution: 5540 = (-9766714092174289)^3 + 9706646342356061^3 + 2*(2044177502818754)^3(2020.2.22)]
[345. New solution: 5540 = (-1274248491925945)^3 + 1094658539478551^3 + 2*(723458325298043)^3(2020.2.22)]
[344. New solution: 3676 = (36330027574363)^3 + (16201371125359)^3 + 2*(-29663565976595)^3(2020.2.22)]
[343. New solution: 3676 = (-1040743660046111)^3 + 1040742887519425^3 + 2*(10786916701381)^3(2020.2.22)]
[342. px^4 + py^4 = 2pu^4 + qv^4 (2020.2.22)]
[341. y^2 = x^3-px (2020.2.5)]
[340. y^2 = x^3+px (2020.2.5)]
[339. x^4 + y^4 - 1 = z^2 Part 2 (2020.1.17)]
[338. x^4 + y^4 - 1 = z^2 (2020.1.1)]
[337. x1^n + x2^n + x3^n = y1^3 + y2^3 + y3^3 (2019.12.9)]
[336. x1^6 + x2^6 + x3^6 = y1^3 + y2^3 + y3^3 (2019.12.6)]
[335. x1^5 + x2^5 + x3^5 = y1^3 + y2^3 + y3^3 (2019.12.4)]
[334. Primitive pythagorean triangles with same perimeter(2019.11.18)]
[333. N-tuples of positive integers with the same sum and the same product  (2019.10.26)]
[332. Pythagorean triangles such that all triangles have same area  (2019.10.2)]
[331. (-74924259395610397)^3 + 72054089679353378^3 + 35961979615356503^3 = 906 (2019.9.24)]
[330. 569936821221962380720^3 +(-569936821113563493509)^3 +(-472715493453327032)^3 = 3 (2019.9.19)]
[329. (-80538738812075974)^3 + (80435758145817515)^3 + (12602123297335631)^3 = 42 (2019.9.14)]
[328. Heron Triangles (2019.9.2)]
[327. ax^4 + by^2 = c (2019.8.26)]
[326. {a^4+b^4+c^4 = d^4+e^4+f^4 ,abc=def} (2019.8.19)]
[325. {a^4+b^4+c^4+d^4 = e^4+f^4+g^4+h^4 ,abcd=efgh} Part 3(2019.8.14)]
[324. {a^4+b^4+c^4+d^4 = e^4+f^4+g^4+h^4 ,abcd=efgh} Part 2(2019.8.12)]
[323. {a^3+b^3+c^3 = d^3+e^3+f^3 , abc=def} (2019.8.8)]
[322. a^3x^6+b^3y^6+ 2z^6 = 2w^6 (2019.7.30)]
[321. x1^4 + 2nX2^4 = X3^8 + n^2X4^8 (2019.7.26)]
[320. ax113 + bx123 + cx133 = ax213 + bx223 + cx233 = ... = axm13 + bxm23 + cxm33 (2019.7.24)]
[319. Generalized Taxicab Number Part 5 (2019.7.17)]
[318. Generalized Taxicab Number Part 4 (2019.7.9)]
[317. Generalized Taxicab Number Part 3 (2019.7.2)]
[316. X^3 + Y^3 + dZ^3 = 0 (2019.6.23)]
[315. a/(b+c+d) +b/(a+c+d) +c/(a+b+d)+ d/(a+b+c) = n (2019.6.10)]
[314. ax^3+ay^3+bz^3+bw^3 = n (2019.5.21)]
[313. ax^3 + by^3 + cz^3 = n (2019.5.14)]
[312. x^5+y^5=cz^2 (2019.5.3)]
[311. ax^3+by^3=cz^3 (2019.4.25)]
[310. New solution: x^3+y^3+z^3=n (2019.3.24)(2019.3.18)(2019.3.17)]
[309. 33 = 8866128975287528^3 -8778405442862239^3 -2736111468807040^3 (2019.3.13)]
[308. ax^3 + by^3 = z^k (2019.2.27)]
[307. ax^4+bx^2y^2+cy^4=dz^2 (2019.2.19)]
[306. {ax^2+by^2=cs^2, ay^2+bx^2=ct^2} (2019.2.22)(2019.2.13)]
[305. ax^4 + by^4 = cz^2 (2019.2.7)]
[304. x^4 + y^4 = cz^2, 40000<=c<50000 (2019.1.30)(2019.1.28)]
[303. x^4 + y^4 = cz^2, 30000<=c<40000 (2019.1.28)]
[302. x^4 + y^4 = cz^2, 20000<=c<30000 (2019.1.23)]
[301. x^4 + y^4 = cz^2, 10000<=c<20000 (2019.1.22)(2019.1.19)(2019.1.16)]
[300. New solution:  7727 = 4677195736433^3 - 1373927732968^3 - 2*3680658132529^3 (2018.12.30)]
[299. {ax^6 + by^6 + cz^6=u^6, bx^6 + cy^6 + az^6=v^6, cx^6 + ay^6 + bz^6=w^6} (2018.12.14)]
[298. {ax^5 + by^5 + cz^5=u^5, bx^5 + cy^5 + az^5=v^5, cx^5 + ay^5 + bz^5=w^5} (2018.12.14)]
[297. {ax^4 + by^4 + cz^4=u^4, bx^4 + cy^4 + az^4=v^4, cx^4 + ay^4 + bz^4=w^4} (2018.12.14)]
[296. {ax^3 + by^3 + cz^3=u^3, bx^3 + cy^3 + az^3=v^3, cx^3 + ay^3 + bz^3=w^3} (2018.12.14)]
[295. {ax^2 + by^2 + cz^2 = u^2, bx^2 + cy^2 + az^2 = v^2, cx^2 + ay^2 +bz^2 = w^2} (2018.12.13)]
[294. ax^3 + by^3 + cz^3 + dw^3 = 0 (2018.11.28)]
[293. Generalized Taxicab Number Part 2 (2018.11.17)(2011.2.1)]
[292. 4x4 magic squares of squares (2018.11.6)]
[291. A^3 + B^3 = n(C^3 + D^3)(2018.10.30)]
[290. Magic hexagon(2018.10.25)]
[289. m(x1^5+x2^5+x3^5+x4^5)=n(y1^5+y2^5+y3^5+y4^5)(2018.10.8)]
[288. m(x1^4+x2^4+x3^4)=n(y1^4+y2^4+y3^4)(2018.10.6)]
[287. m(x1^3+x2^3+x3^3+x4^3)=n(y1^3+y2^3+y3^3+y4^3) Part 2(2018.9.27)]
[286. n^5=a^5+b^5+c^5-d^5-e^5-f^5-g^5(2018.9.13)]
[285. n^4+a^4+b^4=c^4+d^4+e^4(2018.9.12)]
[284. {A^2+B^2=C^2, Ap+Bq=Cr, Bp-Aq=C, p^2+q^2=r^2+1}(2018.9.10)]
[283. m(x1^3+x2^3+x3^3+x4^3)=n(y1^3+y2^3+y3^3+y4^3)(2018.9.8)]
[282. (x+y+z+w)(1/x+1/y+1/z+1/w) = n(2018.8.28)]
[281. (x+y+z+w+s+t)(1/x+1/y+1/z+1/w+1/s+1/t) = n(2018.8.14)]
[280. (x+y+z+w+s)(1/x+1/y+1/z+1/w+1/s) = n Part 2(2018.8.1)]
[279. (x+y+z+w+s)(1/x+1/y+1/z+1/w+1/s) = n(2018.7.26)(2018.7.22)]
[278. x^4+mx^2y^2+y^4=z^2(2018.7.14)]
[277. { x^2+A=u^2, x^2-A=v^2 } Part 2(2018.7.6)]
[276. { x^2+A=u^2, x^2-A=v^2 } (2018.6.29)]
[275. { A+x^2=u^2, A-x^2=v^2 } Part 2(2018.6.26)]
[274. { A+x^2=u^2, A-x^2=v^2 } (2018.6.23)]
[273. New solution:  8968 = 1950774418348^3 + 987248618926^3 - 2*1612528225790^3 (2018.6.15)]
[272. X^4 + Y^4 + Z^8 = 2W^4 (2018.6.6)]
[271. New solution: 1084 = 10617017591719^3 + 2342686574875^3 - 2*8456801802575^3(2018.5.23)]
[270. New solution: 1975 = 36566656985380^3  - 35294370032999^3 -2*13506708241817^3(2018.5.14)]
[269. a^2X^8 + 2ab^4Y^4 + Z^8 = (a+b^4)^2W^4 (2018.5.5)]
[268. New solution:  2372 = 3384145055^3 - 16870920115^3 + 2*13354335746^3 (2018.4.26)]
7862 = 10955159432^3 - 26911887070^3 + 2*20868465863^3
[267. X^5 + aY^5 + aZ^5 = W^2 (2018.4.12)]
[266. Sum of a square and a fourth power in n different ways (2018.4.4)(2018.3.28)(2018.3.24)]
[265. x^n + y^n = z^(n-1) + w^(n-1) (2018.3.14)]
[264. X^3+Y^3+Z^3-nXYZ = (n-3)(n^2+3n+9) (2018.3.6)]
[263. x^7 + az^n = y^7 + aw^n,n=2,3,4,5,6,7 (2018.3.1)]
[262. ax^4 + by^4 + cz^4 + dw^4 + eu^4= 0(2018.2.2)]
[261. New solution: 1121 = 975387209174^3+  493624309463^3 -2*806264112895^3(2018.1.8)]
[260. X^3 + Y^3 + Z^3 + W^3 = 24n^2+2(2018.1.6)]
[259. X^3 + Y^3 + Z^3 + W^3 = 3n^2+3n+1(2018.1.5)]
[258. X^3 + Y^3 + Z^3 + W^3 = 1(2018.1.3)]
[257. x(x+y)(x+2y)(x+3y) = u(u+v)(u+2v)(u+3v)(2017.12.20)]
[256. ax1^4 + bx2^4 = ay1^4 + by2^4, 300<=a<400(2017.12.9)]
[255. ax1^4 + bx2^4 = ay1^4 + by2^4, 200<=a<300(2017.11.17)]
[254. ax1^4 + bx2^4 = ay1^4 + by2^4, 100<=a<200(2017.11.4)]
[253. x^9 + az^8 = y^9 + aw^8(2017.10.24)]
[252. x^9 + az^3 = y^9 + aw^3(2017.10.24)]
[251. x^9 + az^2 = y^9 + aw^2(2017.10.24)]
[250. x^8 + az^7 = y^8 + aw^7(2017.10.19)]
[249. x^8 + az^2 = y^8 + aw^2(2017.10.19)]
[248. x^8 + az^3 = y^8 + aw^3(2017.10.17)]
[247. x^7 + az^3 = y^7 + aw^3(2017.10.12)]
[246. x^7 + az^6 = y^7 + aw^6(2017.10.9)]
[245. x^7 + az^2 = y^7 + aw^2(2017.10.9)]
[244. x^6 + az^6 = y^6 + aw^6(2017.10.5)]
[243. x^6 + az^4 = y^6 + aw^4(2017.9.26)]
[242. x^5 + az^4 = y^5 + aw^4(2017.9.24)]
[241. x^5 + az^3 = y^5 + aw^3(2017.9.24)]
[240. x^5 + az^2 = y^5 + aw^2(2017.9.23)]
[239. New solution:  788 =   4363964249747^3 - 4553874231847^3 + 2*1782603015764^3(2017.9.21)]
1975 =  4645912177207^3 - 4843138985528^3 + 2*1881489396298^3
2300 = -6452934831199^3 + 6730693690883^3 -2*2625897595264^3
[238. New solution: 9463 = 13805037457^3 + 2*30636954619^3 - 39179981372^3(2017.9.15)]
[237. x^6 + az^5 = y^6 + aw^5(2017.9.13)]
[236. x^6 + az^2 = y^6 + aw^2(2017.9.11)]
[235. x^6 + az^3 = y^6 + aw^3(2017.9.7)]
[234. x1^7 + x2^7 + x3^7 + x4^7 = y1^7 + y2^7 + y3^7 + y4^7 + y5^7(2017.9.1)]
[233. ax1^3 + bx2^3 + cx3^3 = ay1^n + by2^n + cy3^n(2017.8.21)]
[232. New solution: 4819 = -7203186652517^3 + 7095691381372^3 + 2* 2019966858598^3(2017.8.9)]
[231. Solution of A^4 + hB^4 = C^4 + hD^4 Part 2(2017.8.2)(2017.7.5)(2013.9.12)(2013.8.17)]
[230. Table of solutions of a^4 + b^4 + c^4 = d^4(2017.7.20)(2017.7.19)]
[229. Table of solutions of a^4 + b^4 + c^4 + d^4 = (a+b+c+d)^4(2017.7.11)]
[228. Solution of A^4 + hB^4 = C^4 + hD^4 Part 2(2017.7.5)(2013.9.12)(2013.8.17)]
[227. Solution of A^4 + hB^4 = C^4 + hD^4, 19000<=h<20000(2017.7.5)]
[226. Solution of A^4 + hB^4 = C^4 + hD^4, 18000<=h<19000(2017.7.5)]
[225. Solution of A^4 + hB^4 = C^4 + hD^4, 17000<=h<18000(2017.6.28)]
[224. Solution of A^4 + hB^4 = C^4 + hD^4, 16000<=h<17000(2017.6.28)]
[223. Solution of A^4 + hB^4 = C^4 + hD^4, 15000<=h<16000(2017.6.17)]
[222. Solution of A^4 + hB^4 = C^4 + hD^4, 14000<=h<15000(2017.6.17)]
[221. Solution of A^4 + hB^4 = C^4 + hD^4, 13000<=h<14000(2017.6.7)]
[220. Solution of A^4 + hB^4 = C^4 + hD^4, 12000<=h<13000(2017.6.7)]
[219. Solution of A^4 + hB^4 = C^4 + hD^4, 11000<=h<12000(2017.5.26)]
[218. Solution of A^4 + hB^4 = C^4 + hD^4, 10000<=h<11000(2017.5.26)]
[217. Solution of A^4 + hB^4 = C^4 + hD^4, 9000<=h<10000(2017.5.14)]
[216. Solution of A^4 + hB^4 = C^4 + hD^4, 8000<=h<9000(2017.5.5)]
[215. Solution of A^4 + hB^4 = C^4 + hD^4 Part 2(2017.5.8)(2017.5.03)(2013.9.12)(2013.8.17)]
[214. Solution of A^4 + hB^4 = C^4 + hD^4, 7000<=h<8000(2017.4.28)]
[213. Solution of A^4 + hB^4 = C^4 + hD^4, 6000<=h<7000(2017.4.22)]
[212. Solution of A^4 + hB^4 = C^4 + hD^4, 5000<=h<6000(2017.4.18)]
[211. ax1^4 + bx2^4 = ay1^4 + by2^4(2017.4.5)(2017.4.1)]
[210. a(1)x1^n + a(2)x2^n +...+ a(n)xn^n=0(2017.3.16)]
[209. {x+y+z=n, x^3+y^3+z^3=n}(2017.3.1)]
[208. X^n + Y^n + Z^n = Square for n=1,2,3(2017.2.26)]
[207. {x^2+y^2+z^2=u^2, x^3+y^3+z^3=v^3}(2017.2.5)]
[206. Solution of A^4 + hB^4 = C^4 + hD^4 Part 3(2016.12.18)]
[205. Solution of A^4 + hB^4 = C^4 + hD^4, 4000<=h<5000   (2016.11.24)]
[204. Solution of A^4 + hB^4 = C^4 + hD^4, 3000<=h<4000   (2016.11.4)]
[203. Solution of A^4 + hB^4 = C^4 + hD^4, 2000<=h<3000   (2016.10.24)]
[202. Solution of A^4 + hB^4 = C^4 + hD^4, 1000<=h<2000   (2016.10.15)]
[201. {y^2+z^2-x^2=p^2, x^2+z^2-y^2=q^2 , x^2+y^2-z^2=r^2}  (2016.9.27)]
[200. {x^2+yz=u^2, y^2+xz=v^2, z^2+xy=w^2}  (2016.9.2)]
[199. {x^2-y^2=u^2, x^2-z^2=v^2, y^2-z^2=w^2}  (2016.8.12)]
[198. Concordant number  (2016.8.4)]
[197. {a^2+b^2=x^2, a^2+c^2=y^2, b^2+c^2=z^2}  (2016.7.22)]
[196. X1^5 + X2^3 +...+ Xn^5=0, n is even and n > 5  (2016.7.12)]
[195. X1^3 + X2^3 +...+ Xn^3=0, n is odd and n >= 5  (2016.7.1)]
[194. X1^3 + X2^3 +...+ Xn^3=0, n is even and n > 3  (2016.6.16)]
[193. {A + B = p^2, A + C = q^2, B + D = s^2, C + D = t^2, B + C = u^2, A + D = v^2}  (2016.6.1)]
[192. Congruent number  (2016.5.6)]
[191. x^4 - y^4 = cz^2  (2016.4.19)]
[190. a + b + c = abc = N  (2016.4.1)]
[189. a^4 + b^4 + c^4 + d^4 = e^4 + f^4 + g^4 + h^4, abcd=efgh  (2016.3.20)]
[188. x^5 + y^3 = z^5 + w^3  (2016.1.29)]
[187. px^n + qy^3 = qz^m + pw^3  (2016.1.3)]
[186. X^4 + Y^4 + Z^4 + W^4 = T^n, n=5,6,7,9  (2015.11.19)]
[185. X^4 + Y^4 + Z^4 + W^4 = T^3  (2015.11.4)]
[184. X^4 + Y^4 + Z^4 + W^4 = T^2 Part 2  (2015.10.9)]
[183. X^4 + Y^4 + Z^4 + W^4 = T^2   (2015.10.2)]
[182. a^4 + b^4 + c^4 + d^4 = (a+b+c+d)^4 Part 3   (2015.8.27)(2015.8.25)(2015.8.13)(2015.8.4)]
[181. a^4 + b^4 + c^4 + d^4 = (a+b+c+d)^4 Part 2   (2015.7.19)]
[180. px^6 + qy^3 = qz^6 + pw^3   (2015.7.1)]
[179. ax1^n + bx2^n + cx3^n = ay1^n + by2^n + cy3^n, n=2,6   (2015.6.1)]
[178. a(1)x1^n + a(2)x2^n +...+ a(k)xk^n = a(1)y1^n + a(2)y2^n +...+ a(k)yk^n   (2015.5.1)]
[177. a6x^6+a5x^5y+a4x^4y^2+a3x^3y^3+a2x^2y^4+a1xy^5+ a0y^6 = a6u^6+a5u^5v+a4u^4v^2+a3u^3v^3+a2u^2v^4+a1uv^5+ a0v^6   (2015.4.2)]
[176. 4036 = 309317704627^3 - 315184953527^3 +   2*95027443732^3   (2015.3.22)]
[175. a4x^4+a3x^3y+a2x^2y^2+a1xy^3+a0y^4 = a4u^4+a3u^3v+a2u^2v^2+a1uv^3+a0v^4  (2015.3.5)]
[174. 9724 =  20018592691^3 -  26097822863^3 +   2*16957680280^3  (2015.2.17)]
[173. Arithmetic progressions on quartic curves  (2015.2.7)]
[172. Arithmetic progressions on cubic curves  (2015.2.7)]
[171. Arithmetic progressions on quadratic curves  (2015.2.7)]
[170. ax^8 + by^8 + cz^4 + dw^4 = 0  (2015.2.1)]
[169. Happy New Year!   (2015.1.1)]
[168. ax^6 + by^6 + cz^6 + dw^3 = 0  (2014.12.3)]
[167. w^2 = x^6 + y^6 + z^6 Part 2  (2014.11.19)]
[166. w^2 = x^6 + y^6 + z^6  (2014.11.18)]
[165. X^n + Y^n = square for n=1, 2, 3  (2014.11.1)]
[164. ax^6 + by^6 + cz^6 = w^2 and ax^6 + by^6 + cz^6 = w^3  (2014.10.10)]
[163. x^3 + y^3 + z^3 = n  (2014.9.9)]
[162. ax^5 + by^5 + cz^5 = w^2 Part 2  (2014.8.19)]
[161. ax^6 + by^6 + cz^6 = w^2  (2014.8.7)]
[160. ax^5 + by^5 + cz^5 = w^2  (2014.7.28)]
[159. ax^4 + by^4 + cz^4 = w^2  (2014.7.22)]
[158. x^2 + y^2 = z^n + w^n and x^3 + y^3 = z^n + w^n  (2014.7.11)]
[157. Solution of ax^4 + by^4 + cz^4 + dw^4 = 0 Part 2  (2014.7.4)]
[156. Equal Sums of Sixth Powers  (2014.6.1)]
[155. Solution of ax^4 + by^4 + cz^4 + dw^4 = 0  (2014.5.1)]
[154. Any rational number N is the sum and difference of four rational fourth powers
in an infinite number of ways Part 2  (2014.4.5)]
[153. Equal Sums of Eighth Powers  Part 5  (2014.3.3)]
[152. Solutions  of  x^3 + y^3 + z^3 = t^n  Part 2  (2014.1.31)]
[151. Happy New Year!   (2014.1.1)]
[150. Solution of sextic diophantine equation(2013.11.1)]
[149. Solution of x^3 + dy^3 + d^2z^3 - 3dxyz = 1(2013.9.28)]
[148. Solution of A^4 + hB^4 = C^4 + hD^4 Part 2(2013.9.12)(2013.8.17)]
[147. Solution of A^4 + hB^4 = C^4 + hD^4  (2013.8.1)]
[146. Solution of X^k + Y^k = {U^2,V^4} for k=1,2  (2013.7.12)]
[145. Three positive numbers such that the sum and difference of any two are squares  (2013.6.14)]
[144. Four positive numbers such that the sum of any two is a cube  (2013.5.15)]
[143. Solutions of x^4 + ax^2y^2 + y^4 = u^4 + au^2v^2 + v^4  (2013.5.1)]
[142. Solutions of x^4 + ay^4 = z^4 + bt^4  (2013.4.1)]
[141. Solutions of x^2 + y^4 = 5z^4  (2013.3.1)]
[140. A parametric solution of X^k + Y^k + Z^k + W^k + S^k = {U^2,V^4} for k=2,4  (2013.2.1)]
[139. Happy New Year!   (2013.1.1)]
[138. Equal Sums of Seventh Powers  (2012.11.30)]
[137. Many solutions of n=x^3 + y^3 + 2z^3  (2012.10.18)(2012.9.24)]
[136. Solutions of ax^6 + by^3 = cz^2  (2012.9.10)]
[135. Equal Sums of Eighth Powers  Part 4  (2012.8.10)]
[134. New solution:  4388 = -18105946705^3 + 18108094211^3 - 2*1018372219^3  (2012.7.12)]
[133. Solutions  of  x^4 + y^4 + z^4 = w^2    (2012.7.2)]
[132. Equal Sums of Eighth Powers  Part 3    (2012.6.11)]
[131. A collection of the parametric solutions for equal sums of sixth powers    (2012.5.3)]
[130. A collection of the parametric solutions for equal sums of fifth powers    (2012.4.2)]
[129. Equal Sums of Fifth Powers    (2012.3.2)]
[128. Equal sums and equal products    (2012.2.1)]
[127. Happy New Year!    (2012.1.3)]
[126. Any non-zero rational number m is the sum of three rational cubes
in an infinite number of non-trivial ways.  (2011.12.6)]
[125. New parametric solutions of x^3 + y^3 + z^3 = t^2  (2011.11.16)]
[124. Equal Sums of Eighth Powers et 1  (2011.10.11)]
[123. Equal Sums of Fourth Powers et 1  (2011.9.13)]
[122. Equal Sums of Fifth Powers et 1  (2011.8.23)]
[121. Equal Sums of Sixth Powers et 1  (2011.8.1)]
[120. Equal Sums of Seventh Powers et 1  (2011.7.18)]
[119. Equal Sums of Eighth Powers   (2011.7.1)]
[118. Solutions  of  x^4 + y^4 + z^4 = w^n   (2011.6.3)]
[117. EQUAL SUMS OF ELEVENTH POWERS   (2011.5.6)]
[116. Solutions  of  x^4 + y^4 + z^4 = nw^3   (2011.4.1)]
[115. EQUAL SUMS OF SEVENTH POWERS   (2011.3.4)]
[114. New solution:  3047 =  234115946^3  -  81713665^3 - 2* 183146068^3  (2011.2.16)]
[113. Generalized Taxicab Number Part 2  (2011.2.1)]
[112. Happy New Year!    (2011.1.1)]
[111. Generalized Taxicab Number   (2010.12.3)]
[110. x1^4 + x2^4 +...+ xn^4 = nw^2  (2010.11.1)]
[109. ON EQUAL SUMS OF NINTH POWERS  Part 2  (2010.10.1)]
[108. Solutions  of  x^4 + y^4 + z^4 = nw^2  (2010.9.1)]
[107. Any rational number N is the sum and difference of four rational fourth powers
in an infinite number of ways.  (2010.8.1)]
[106. ON EQUAL SUMS OF NINTH POWERS  (2010.7.20)]
[105. Solutions  of  x^4 + y^4 = cz^2  (2010.8.6)(2010.8.5)(2010.7.1)]
[104. Solutions  of  X^3 + Y^3 + Z^3 = mW^3  (2010.6.1)]
[103. 3956=    3481598477^3  -  1323591649^3 - 2*  2711779804^3  (2010.5.11)]
8779=   64325766916^3  - 11325451823^3 - 2* 50962343435^3
[102. Solutions  of  x3 + y3 + z3 = tn  (2010.5.1)]
[101. A4+ B4+ C4 = D4+ E4  Part 2  (2010.4.10)]
[91.　Solutions of a^4 + b^4 + c^4 + d^4 = (a+b+c+d)^4    (2010.4.11)(2010.4.7)(2010.4.2)(2009.7.30)(2009.7.12)]
[100. x^4 + ay^4 = z^4 + bt^4 (2010.3.31)]
[99.　1 = (4x^4 + 1)^4 -(4x^4)^4 -(4x^3)^4 -(2x)^4 -(3x^2)^4 -(2x^2)^4 +(x^2)^4 (2010.3.26)]
[98.　2 = (8x^5-2x)^4 + (8x^4+1)^4 + (8x^4-1)^4 - (8x^5+2x)^4 - (4x^2)^4 (2010.3.10)]
[97.　Ramanujan's identity (4x^5-5x)^4 + (6x^4-3)^4 + (4x^4+1)^4 - (4x^5+x)^4 - (2x^4-1)^4 = 81 (2010.3.3)]
[70.　Solutions  of  a15+a25+a35 = b15+b25+b35   (2010.2.12) (2008.5.1)]
[96.　Repunit    (2010.1.13)]
[95.　A Happy New Year!    (2010.1.1)]
[94.　On factors of Mersenne numbers.    (2009.12.10)]
[93.　Solutions  of  X4 + Y4 = 4481Z2.    (2009.11.1)]
[92.　Smallest number that is a sum of two n-th powers of positive
rationals but not of two n-th powers of positive integers.  (2009.9.6)]
[91.　Solutions of a^4 + b^4 + c^4 + d^4 = (a+b+c+d)^4    (2009.7.30)(2009.7.12)]
[90.　Solutions  of  a16+a26+a36 = b16+b26+b36    (2009.6.26)]
[89.　Representation by fourth powers  Part 2    (2009.6.15)]
[88.  9033964577482532388059482429398457291004947925005743028147465732645880^4 +
4417264698994538496943597489754952845854672497179047898864124209346920^4 +
1439965710648954492268506771833175267850201426615300442218292336336633^4 =
9161781830035436847832452398267266038227002962257243662070370888722169^4  (2009.6.1)]
[87.　Representation by fourth powers     (2009.5.1)]
[86.　A4+ B4+ C4+ D4+ E4= F4 (Ramanujan's identities, again x 2)  (2009.3.16)]
[85.　x4+y4+z4 = nw4    (2009.3.1)]
[84.　A4=B4+C4+D4+E4    (2009.2.10)]
[83.　A Happy New Year!    (2009.1.1)]
[82.　Table of the solutions for x3+by3+cz3=0.  (2008.12.3)]
[81.　Every integer is a sum of four cubes of integers?  (2008.11.1)]
[80.　Table of the solutions for A4+B4+C4=D4  Part 2  (2008.10.5)]
[79.　1300643009914004+ 4408049425801604+ 5148181012992894= 5736463218719614  (2008.9.15)]
[78.　Table of the solutions for A4+B4+C4=D4  (2008.9.1)]

[77.　12597684734=11667058404+8593964554+5889033364  (2008.9.1)]
8738221214=7693212804+6067108714+5584244404
17878823374=16629976634+12377969604+6863980004
18717138574=15935130804+15535564404+926224014

[76.　478867402721149764 + 88134256704402404 + 568278133081117854 = 629405169034106014  (2008.8.13)]
35790871473754404 +148900264334684714 + 185659451142167204 = 202495067095797214  (2008.8.13)]
[75.　New solutions of n=x3+y3+2z3  (2009.1.15)(2008.7.31)(2008.7.13)(2008.6.22)]
[74.　Solve the Diophantine equation like Diophantus    (2008.6.15)]
[73.　N=5,6,and 7 mod 8 is always a congruent number    (2008.6.1)]
[72.　49875884196554+24804526756004+5020388539764=50622976992574    (2008.5.15)]
[71.　4 + 27 = 31!?    (2008.5.12)]
[70.　Solutions  of  a15+a25+a35 = b15+b25+b35    (2008.5.1)]
[69.　Sierpinski problem    (2008.4.11)]
[68.　Sums of three cubes    (2008.2.7)(2008.1.15)(2008.1.8)(2008.1.5)]

[67.　A Happy New Year!    (2008.1.1)]
[66.　58219814004+153558313604+1409765514=154345478014  (2007.10.24)]
[65.　A16+ A26+ ....+ A66 = B16+ B26+ ....+ B66        (2007.10.15)]
[64.　A16+ A26+ ....+ A56 = B16+ B26+ ....+ B56        (2007.10.15)]
[63.　EQUAL SUMS OF SEVENTH POWERS        (2007.8.20)(2007.10.15)]

```

テーマ
リンク集

1.　x3+y3+z3　の問題　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　続く

2.　素数を生成する３次多項式(2005.4.10)

3.　x
3+y3+z3＝w
3のパラメータ解(2005.4.26)

4.　ガウス讃、或いは温故知新(2005.5.5)

5.　Demjanenko的恒等式(2005.5.10)

6.　オイラー敗れたり！(2005.5.22)(2005.6.13)

7.　インド人もビックリ！？(2005.6.16)

8.　続インド人もビックリ！？(2005.6.19)

9.　A4+B4+C4 = D4+E4+F4 　(2005.6.25)

10.　続A4+B4+C4 = D4+E4+F4 　(2005.7.15)

11.　和の世界 　(2005.7.17)

12.　A5+B5+C5 = D5+E5+F5 　(2005.8.14)

13. ＵＢＡＳＩＣ超入門 　(2005.8.18)

14. ５乗数的有楽 　(2005.8.21)

15. タクシーナンバーと楕円曲線 　(2005.9.25) mail: 