# Newer sums of three cubes

@article{Huisman2016NewerSO, title={Newer sums of three cubes}, author={Sander G. Huisman}, journal={arXiv: Number Theory}, year={2016} }

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 reported. This only leaves $k=33$ and $k=42$ for $k<100$ for which no solution has yet been found. A total of 966 new solutions were found.

## 6 Citations

Hilbert's Tenth Problem: Refinements and Variants

- Mathematics
- 2021

Hilbert’s 10th problem, stated in modern terms, is Find an algorithm that will, given p ∈ Z [ x 1 , . . . , x n ] , determine if there exists a 1 , . . . , a n ∈ Z such that p ( a 1 , . . . , a n ) =…

Cracking the problem with 33

- MathematicsResearch 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…

1 Hilbert ’ s Tenth Problem

- Mathematics
- 2021

Hilbert’s 10th problem, stated in modern terms, is Find an algorithm that will, given p ∈ Z[x1, . . . , xn], determine if there exists a1, . . . , an ∈ Z such that p(a1, . . . , an) = 0. Davis,…

Hilbert's Tenth Problem

- MathematicsSIGACT News
- 2021

This column is a short version of a long version of an article based on a blog. What? I give the complete history.

On a question of Mordell

- MathematicsProceedings of the National Academy of Sciences
- 2021

This paper concludes a 65-y search with an affirmative answer to Mordell’s question and strongly supports a related conjecture of Heath-Brown and makes several improvements to methods for finding integer solutions to x3+y3+z3=k for small values of k.

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.

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