# New integer representations as the sum of three cubes

```@article{Beck2007NewIR,
title={New integer representations as the sum of three cubes},
author={Michael Beck and Eric Pine and Wayne Tarrant and Kim Yarbrough Jensen},
journal={Math. Comput.},
year={2007},
volume={76},
pages={1683-1690}
}```
• Published 14 March 2007
• Mathematics, Computer Science
• Math. Comput.
We describe a new algorithm for finding integer solutions to x 3 + y 3 + z 3 = k for specific values of k. We use this to find representations for values of k for which no solution was previously known, including k = 30 and k = 52.
12 Citations
New sums of three cubes
• Mathematics
Math. Comput.
• 2009
The search for solutions of the Diophantine equation x 3 + y 3 + z 3 = n for n < 1000 and |x|, |y |, |z| < 10 14 is reported on.
AN OBSERVATION CONCERNING THE REPRESENTATION OF POSITIVE INTEGERS AS A SUM OF THREE CUBES
• Mathematics
• 2021
In recent years there has been significant progress on the problem of representing integers as a sum of three cubes. Most significantly are the relatively new solutions found by Booker and Sutherland
Existential refinement on the search of integer solutions for the diophantine equation \$x^3+y^3+z^3=n\$
• Mathematics
• 2021
We propose a new algorithm, call S.A.M to determinate the existence of the solutions for the equation x 3 + y 3 + z 3 = n for a ﬁxed value n > 0 unknown.
The search of solutions of the Diophantine equation \$x^3 + y^3 + z^3 = k\$ for \$k<1000\$ has been extended with bounds of \$|x|\$, \$|y|\$ and \$|z|\$ up to \$10^{15}\$. The first solution for \$k=74\$ is
A New Method in the Problem of Three Cubes
• Mathematics
• 2017
In the current paper we are seeking P1(y); P2(y); P3(y) with the highest possible degree polynomials with integer coefficients, and Q(y) via the lowest possible degree polynomial, such that = Q(y).
HOW TO SOLVE A DIOPHANTINE EQUATION
We introduce Diophantine equations and show evidence that it can be hard to solve them. Then we demonstrate how one can solve a specific equation related to numbers occurring several times in
Cracking the problem with 33
• A. Booker
• Mathematics
Research in Number Theory
• 2019
Inspired by the Numberphile video "The uncracked problem with 33" by Tim Browning and Brady Haran, we investigate solutions to \$x^3+y^3+z^3=k\$ for a few small values of \$k\$. We find the first known
The Heterogeneity of Mathematical Research
If the authors wish to construct formal-logical models of mathematical practices, taking into account the maximum of detail, then it is a wise strategy to see mathematics as a heterogeneous entity, according to the core thesis of this contribution.
Sums of integer cubes
• S. Siksek
• Medicine
Proceedings of the National Academy of Sciences
• 2021