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arXiv · 2203.08671

Additive decompositions of cubes in finite fields

Hai-Liang Wu·Yue-Feng She
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Abstract

Let $p\equiv1\pmod3$ be a prime . We study several topics on additive decompositions concerning the set $C_p$ of all non-zero cubes in the finite field of $p$ elements. For example, we show that when $p>184291$ , the set $C_p$ has no decomposition of the form $C_p=A+B+C$ with $|A|,|B|,|C|\ge2$.

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Hai-Liang Wu, Yue-Feng She. 2022-03-16. Additive decompositions of cubes in finite fields. https://arxiv.org/abs/2203.08671

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