Details

Autor(en) / Beteiligte

• Chen, Yong-Gao
• Yan, Xiao-Hui

Titel

A conjecture of Sárközy on quadratic residues

Ist Teil von

• Journal of number theory, 2021-12, Vol.229, p.100-124

Ort / Verlag

Elsevier Inc

Erscheinungsjahr

2021

Link zum Volltext

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• For any prime p, let Rp be the set of all quadratic residues modulo p. In 2012, Sárközy proved that if p is a sufficiently large prime, then Rp has no 3-decomposition A+B+C=Rp with |A|,|B|,|C|≥2. In this paper, we prove that for any prime p, Rp has no additive 3-decomposition A+B+C=Rp with |A|,|B|,|C|≥2. Furthermore, for any prime p, if A+B=Rp is a 2-decomposition, then 0.17p+1<|A|,|B|<2.8p−6.63. We also pose three related conjectures.