Additive decompositions of cubes in finite fields

• DOI: 10.1007/s11139-022-00690-1
• Publication Date: 2023-02-17T05:48:02Z
• Authors: Hai-Liang Wu; Yue-Feng She
• Keywords: Zero (linguistics); Finite set

13 Pages<br/>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 $|A|,|B|,|C|\ge2$.<br/>