It is proved that there is no Sidon set selected from {1, 2, ... , N} whose sum set contains c(1)N(1/2) consecutive integers, but it may contain c(2)N(1/3) consecutive integers. Moreover, it is shown that a finite Sidon set cannot be well-covered by generalized arithmetic progressions.
机构:
Yangzhou Univ, Sch Math Sci, Yangzhou 225002, Jiangsu, Peoples R China
Yangzhou Univ, Inst Math, Yangzhou 225002, Jiangsu, Peoples R ChinaYangzhou Univ, Sch Math Sci, Yangzhou 225002, Jiangsu, Peoples R China
机构:
Univ Paris VIII, Dept Math, F-93526 St Denis, France
Univ Paris XIII, Sorbonne Paris Cite, CNRS, LAGA,UMR 7539, F-93430 Villetaneuse, France
Telecom Paris, F-91120 Palaiseau, FranceUniv Paris VIII, Dept Math, F-93526 St Denis, France