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
-------
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.
-----------
-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}
-------
----