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Đề tài "The Erd˝os-Szemer´edi problem on sum set and product set"

Chia sẻ: Nnguyen Nhi | Ngày: | Loại File: PDF | Số trang:20

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The basic theme of this paper is the fact that if A is a finite set of integers, then the sum and product sets cannot both be small. A precise formulation of this fact is Conjecture 1 below due to Erd˝s-Szemer´di [E-S]. (see also [El], [T], o e and [K-T] for related aspects.) Only much weaker results or very special cases of this conjecture are presently known. One approach consists of assuming the sum set A + A small and then deriving that the product set AA is large (using Freiman’s structure theorem) (cf. [N-T], [Na3]). We follow the...

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