@article{Siksek2021SumsOI,
title={Sums of integer cubes},
author={Samir Siksek},
journal={Proceedings of the National Academy of Sciences},
year={2021},
volume={118}
}

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.Expand

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… Expand

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The weak approximation principal fails for the forms x + y + z = kw, when k = 2 or 3. The question therefore arises as to what asymptotic density one should predict for the rational zeros of these… Expand