Abstract
We make several improvements to methods for finding integer solutions to x3+y3+z3=k for small values of k. We implemented these improvements on Charity Engine’s global compute grid of 500,000 volunteer PCs and found new representations for several values of k, including 3 and 42. This completes the search begun by Miller and Woollett in 1954 and resolves a challenge posed by Mordell in 1953.
Publisher
Proceedings of the National Academy of Sciences
Reference19 articles.
1. The density of zeros of forms for which weak approximation fails;Heath-Brown;Math. Comp.,1992
2. On the integer solutions of the equation
x
2
+
y
2
+
z
2
+
2
x
y
z
=
n;Mordell;J. London Math. Soc.,1953
3. Solutions of the Diophantine equation
x
3
+
y
3
+
z
3
=
k;Miller;J. London Math. Soc.,1955
4. Cracking the problem with 33;Booker;Res. Number Theory,2019
5. On solving the Diophantine equation
x
3
+
y
3
+
z
3
=
k
on a vector computer;Heath-Brown;Math. Comp.,1993
Cited by
6 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献
1. John William Scott (‘Ian’) Cassels. 11 July 1922 — 27 July 2015;Biographical Memoirs of Fellows of the Royal Society;2023-03-29
2. AN OBSERVATION CONCERNING THE REPRESENTATION OF POSITIVE INTEGERS AS A SUM OF THREE CUBES;Rocky Mountain Journal of Mathematics;2023-02-01
3. Cambricon-P: A Bitflow Architecture for Arbitrary Precision Computing;2022 55th IEEE/ACM International Symposium on Microarchitecture (MICRO);2022-10
4. On the smallest open Diophantine equations;ACM SIGACT News;2022-04-18
5. Sums of integer cubes;Proceedings of the National Academy of Sciences;2021-03-30