• Corpus ID: 119130221

# Newer sums of three cubes

@article{Huisman2016NewerSO,
title={Newer sums of three cubes},
author={Sander G. Huisman},
journal={arXiv: Number Theory},
year={2016}
}
• S. Huisman
• Published 26 April 2016
• Mathematics
• arXiv: Number Theory
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
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• A. Booker
• Mathematics
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• 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
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On a question of Mordell
• Mathematics
Proceedings 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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