Sums of three cubes
https://en.wikipedia.org/wiki/Sums_of_three_cubes
Wikipedia article (English)
Ref.A1
Summe von drei Kubikzahlen
https://de.wikipedia.org/wiki/Summe_von_drei_Kubikzahlen
Wikipedia article (German)
Ref.A2
Cubic Number
https://mathworld.wolfram.com/CubicNumber.html
Wolfram MathWorld article
Ref.A3
Numbers that are not congruent to 4 or 5 mod 9
https://oeis.org/A060464
OEIS A060464
Ref.A4
Sums of integer cubes
https://www.pnas.org/doi/10.1073/pnas.2103697118
by Samir Siksek
Published March 30, 2021
Ref.A5
Why the Sum of Three Cubes Is a Hard Math Problem
https://www.quantamagazine.org/why-the-sum-of-three-cubes-is-a-hard-math-problem-20191105/
by Patrick Honner
November 5, 2019
Ref.A6
Hilbert's tenth problem
https://en.wikipedia.org/wiki/Hilbert%27s_tenth_problem
Wikipedia article (English)
This topic is quoted in the Numberphile Video '3 as the sum of the 3 cubes' (@ 4:10)
Ref.A7
The uncracked problem with 33
https://www.youtube.com/watch?v=wymmCdLdPvM
Youtube Numberphile Video
Ref.B1
74 is Cracked
https://www.youtube.com/watch?v=_-M_3oV75Lw
Youtube Numberphile Video
Ref.B2
42 is the new 33
https://www.youtube.com/watch?v=ASoz_NuIvP0
Youtube Numberphile Video
Ref.B3
The Mystery of 42 is Solved
https://www.youtube.com/watch?v=zyG8Vlw5aAw
Youtube Numberphile Video
Ref.B4
3 as the sum of 3 cubes
https://www.youtube.com/watch?v=GXhzZAem7k0
Youtube Numberphile Video
Ref.B5
569936821221962380720
https://www.youtube.com/watch?v=vv0bHK44Q1s
Youtube Numberphile Video
Ref.B6
SUM OF THREE CUBES (irrational solutions)
https://www.youtube.com/watch?v=KkHGFLiEltE
Youtube Video
by Sir Manny L. Isip
Ref.B7
SUMS OF THREE CUBES (Sutherland_Recording)
https://drive.google.com/file/d/1SgOE6Zzy0mJT7omDF_9txd7yWYAxw-IH/view
A google m4v video
by Andrew V. Sutherland (Number Theory Web seminar, May 2020)
Ref.B8
List of solutions of x^3 + y^3 + z^3 = k for k < 1000
https://mysite.science.uottawa.ca/gwalsh/sumofthreecubes20160426.txt
by Sander G. Huisman
26-04-2016
Ref.C1
List of solutions of x^3 + y^3 + z^3 = k for k < 10000
https://gist.githubusercontent.com/Centrinia/51789c2ebdbc74098faefc7cdf68e1a4/raw/
      5a2de09780b3310a58c10a493f67298dfdf1335f/threecubes.txt

https://gist.github.com/Centrinia/51789c2ebdbc74098faefc7cdf68e1a4
x3 + y3 + z3 = k for k < 5130
Last active 5 years ago !
by Josh Liu (Centrinia)
Ref.C2
Primitieve gehele oplossingen van x^3+y^3+z^3=n (n in [1..1000])
http://www.kaynet.or.jp/~kay/misc/aa3-1000.html
by Hisayasu Nakao
2022.01.15
Ref.C3
Solutions of n=x3+y3+z3
How to search the solutions of n=x3+y3+z3 for 0 ⩽ n ⩽ 10000
Partial listings :
Solutions of n=x3+y3+z3 for 0 ⩽ n ⩽ 99
Solutions of n=x3+y3+z3 for 100 ⩽ n ⩽ 199
ooo
Solutions of n=x3+y3+z3 for 800 ⩽ n ⩽ 899
Solutions of n=x3+y3+z3 for 900 ⩽ n ⩽ 1000

Solutions of n=x3+y3+z3 for 0 ⩽ n ⩽ 1000

by Hisanori Mishima
Last updated around 2010
Ref.C4
Sums of cubes
https://math.mit.edu/~drew/sumsofcubes.html
Results from Andrew R. Booker & the Charity Engine
Ref.C5
threecubes
http://cr.yp.to/threecubes.html
by Daniel J. Bernstein
Results (n < 1000) from the year 2001 → http://cr.yp.to/threecubes.html/20010729
Ref.C6
Solutions of the Diophantine Equation x3+y3+z3=k
https://tomrocksmaths.com/wp-content/uploads/2022/10/journal-of-london-math-soc-january-1955-miller-
      solutions-of-the-diophantine-equation-x3-y3-z3-k.pdf

by J.C.P. Miller and M.F.C. Woollett
January 1955
Ref.D1
Undecidability in Number Theory (pages 1 up to 4)
https://www.cs.drexel.edu/~kn33/cs525_winter_2015_e/
      Undecidability%20%20in%20%20Number%20Theory.pdf

by Bjorn Poonen
2008-2010
Ref.D2
On Sums of Three Integral Cubes
https://personal.science.psu.edu/lxv1/113P.pdf
Pennstate- Department of Mathematics
by W. Conn & N. Vaserstein
March 1992
Ref.D3
On Solving the Diophantine Equation x3 + y3 + z3 = k on a Vector Computer
http://euler.free.fr/docs/HLR93.pdf
D.R. Heath-Brown, W.M. Lioen and H.J.J. te Riele
Mathematics of Computation 61 (203), Juli 1993, S. 235–244
Ref.D4
Newer Sums of Three Cubes
https://arxiv.org/pdf/1604.07746.pdf
by Sander G. Huisman
26 apr 2016
Ref.D5
Solutions of the Diophantine Equation x3 + y3 = z3 – d
https://cr.yp.to/bib/1964/gardiner.pdf
by V.L. Gardiner; R.B. Lazarus; P.R. Stein
Mathematics of Computation, Vol. 18, No.87 (Jul., 1964), 408-413.
March 20, 2004
Ref.D6
Sums of three cubes
https://math.mit.edu/~drew/NTW2020.pdf
by Andrew Sutherland
May 7, 2020
Ref.D7
The Density of Zeros of Forms for which Weak Approximations Fails
https://www.researchgate.net/publication/237335750_       The_Density_of_Zeros_of_Forms_for_which_Weak_Approximation_Fails
From that page you can download the pdf file named [wa.pdf]
by D. Roger Heath-Brown
1992
Ref.D8
Cracking the problem with 33
https://people.maths.bris.ac.uk/~maarb/papers/cubesv1.pdf
By Andrew R. Booker
2019
Ref.D9
On the Integer Solutions of the Equation x2+y2+z2+2xyz = n
https://londmathsoc.onlinelibrary.wiley.com/doi/abs/10.1112/jlms/s1-28.4.500
This pdf file is alas behind a paywall.
If someone can send me a copy of this pdf file I would be most obliged.
This paper is quoted in the Numberphile Video '3 as the sum of the 3 cubes' (@ 0:55)
and briefly in the Numberphile Video '569936821221962380720' (@ 3:20)
by L.J. Mordell
1 oct 1953
Ref.D10
Schakelaar
\(\mathbf[0\gets\to1000\mathbf]\)
Allemaal Getallen


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Laatste update 17 juni 2024