Squarefree numbers in sumsets

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• 作者：Tomasz Schoen
• 关键词：s ; Abelian group ; Dual group ; Partial s-homomorphism ; Approximate extension ; Ulam's problem ; Integral point lattice ; Dual lattice
• 刊名：Indagationes Mathematicae
• 出版年：2005
• 出版时间：20 June 2005
• 年：2005
• 卷：16
• 期：2
• 页码：251-265
• 全文大小：604 K

文摘

We solve a problem of Filaseta by proving, that if N is sufficiently large, A [N], |A| > N/9 and A + Adoes not contain any squarefree integer then all elements of A are congruent to 0 (mod 4) or 2 (mod 4). In order to show the main result we characterize the structure of all dense sets, whose elements sum to no squarefree number.