# cubes

http://www.mathpages.com/home/kmath071.htm

From andrew@sophie.math.uga.edu Fri Nov  3 11:40 EST 2000
Date: Fri, 3 Nov 2000 11:40:47 -0500 (EST)
From: Andrew Granville <andrew@sophie.math.uga.edu>
To: vstein@math.psu.edu
Subject: sums of three cubes
Content-Type: text
Content-Length: 223

(-283,059,965  ,  -2,218,888,517   ,   2,220,422,932).
for 30

also

52 = 60702901317^3 + 23961292454^3 + (-61922712865)^3

the students names are eric pine, mike beck, wayne tarrant and kim yarborough

andrew granville
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Thomas Womack    http://www.tom.womack.net/

http://www.maths.nott.ac.uk/personal/pmxtow/maths.htm

Accordingly, my main interest is Diophantine equations, where, whilst the machinery required to obtain a result
like958004+2175194+4145604=4224814 or 22204229323 - 2830599653 - 22188885173 = 30 can be quite complicated -
the first result comes from an existence proof by Elkies using elliptic curves and extending a result of Demjanenko,
followed by a search on a massively parallel supercomputer by Frye; the second was found by a fairly straightforward
search by four graduate students at the University of Georgia and separately by Elkies&Bernstein by a more sophisticated
method involving approximating the surface x3=y3+z3 by a series of cuboids and using lattice reduction - the result can be
explained to anyone capable of handling multiplication and addition.
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-4352032313 +   4352030833 + 43811593 =75
(* math enc. cubes  Bau, pers. comm., July 30, 1999*)

1173673 +   1344763       -1593803 = 39
http://www.asahi-net.or.jp/~KC2H-MSM/mathland/math04/matb0100.htm
Hisanori Mishima
H.Mishima's page

-29010966943      -155505555553    + 155841398273 = 24
D. J. Bernstein (07/29/2001) http://cr.yp.to/threecubes.html
D. J. Bernstein. Enumerating solutions to p(a)+q(b)=r(c)+s(d). Mathematics of
Computation 70 (2001), 389-394
{-2901096694,      -15550555555,     15584139827,  -2}

396184514443  -87284087913  -394767274183 =81
http://cr.yp.to/threecubes/20010729
{-39476727418,   -8728408791,  39618451444,   -3}

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w3 + x3 + y3 + z3 = 0  Elkies
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