### 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
0 <= n <= 99, not equal 4 or 5 (mod 9) , 0 <= |x| <= |y| <= |z| <= 1010

nxyz
0000
1001
2011
3111
6-1-12
70-12
8002
9012
10112
11-2-23
12710-11
15-122
16-511-16091626
17122
18-1-23
190-23
201-23
21-11-1416
* 24-2901096694-1555055555515584139827
25-1-13
260-13
27003
28013
29113
* 30-283059965-22188885172220422932
33???
34-123
35023
36123
370-34
381-34
* 39117367134476-159380
42???
43223
44-5-78
452-34
46-233
4767-8
48-23-2631
51602659-796
* 522396129245460702901317-61922712865
53-133
54-7-1112
55133
56-11-2122
571-24
60-1-45
610-45
62233
630-14
64004
65014
66114
692-45
701120-21
71-124
7279-10
73124
74???
* 754381159435203083-435203231
782653-55
79-19-3335
8069241103532-112969
811017-18
82-11-1114
83-234
* 84-8241191-4153172641639611
87-1972-41264271
883-45
8966-7
90-134
91034
92134
93-5-57
961085313139-15250
97-1-35
980-35
99234

* 24 : D. J. Bernstein (July 29, 2001) http://cr.yp.to/threecubes.html
* 30 : Eric Pine, Kim Yarbrough, Wayne Tarrant and Michael Beck, University of Georgia
Noam D. Elkies,Rational points near curves and small
nonzero |x3-y2| via lattice reduction
,
ANTS IV (2000) * 39 : D. R. Heath-brown, W. M. Lioen, and H. J. J. Te Riele,On Solving the Diophantine Equation x3+y3+z3=k on a Vector Computer, Math. Comp. 61(1993),235-244.
* 52 : Eric Pine, Kim Yarbrough, Wayne Tarrant and Michael Beck, University of Georgia
* 75 : Andrew Bremner (1993)
* 84 : B. Conn and L. Vaserstein, On sums of three integral cubes, Contemp. Math. 166 (1994), 285-294.

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Hisanori Mishima