### n=x3+y3+z3

D5 Sum of four cubes.
in Richard K. Guy, "Unsolve Problems in Number Theory" Second Edition, Springer-Verlag, 1994

Solutions of n=x3+y3+z3
700 <= n <= 799, not equal to 4 or 5 (mod 9) , 0 <= |x| <= |y| <= |z| <= 1010

nxyz
7001114-15
701458
7022171845-1846
7031-39
704-23-6566
7052411078-1082
708-2833-42434628
709-13-2123
7102-39
7112631-36
712-37-5661
713377
714-14-2325
717-34-115116
71811823293-3343
719-1402-1749717500
720-1-29
7210-29
7221-29
7235864-77
726-772-8771043
727-168
7280-19
729168
730-578
731119
732???
* 7358152382001076499359-1214029864
736-129
737029
738129
739-9-913
7407-1112
* 744-48358933-164458930165841061
745229
7461720-23
747-70-338339
748-239
749-8-2021
750477
753-4-1617
* 754-238441-253285310050
755368
7565-1415
757139
* 758662325744409109962567936-663334553003
7594379-83
762558
7636-1314
764239
7658906853-6858
766-349
* 767506339860536774887-657680046
* 768-496589-19377231948534
771-40-5259
772-6-711
7733093-94
7743361-64
775667
776-11-2627
* 777-1005823-39127593934790
780-13-3132
781-358-940957
7825-710
783-1-610
7841113-14
785-249
* 7861279138731721050373397-22519801850
* 789189181179579264836228687485-19022888796058
790-459
791-478
792-149
793049
794149
795???
7981417-19
799444506-601

* 754, 777 : Elkies (1996)
* 735, 744, 767, 768, 786 : D. J. Bernstein (July 29, 2001) http://cr.yp.to/threecubes.html
* 758, 789 : Leonid Durman (April 19, 2007)
http://www.uni-math.gwdg.de/jahnel/linkstopaperse.html
http://www.uni-math.gwdg.de/jahnel/Arbeiten/Liste/threecubes_20070419.txt

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Hisanori Mishima