An improved lower bound related to the Furstenberg-Sarkozy theorem

作者：Lewko Mark^*

来源：Electronic Journal of Combinatorics, 2015, 22(1): P1.32.

Let D (n) denote the cardinality of the largest subset of the set {1, 2,..., n} such that the difference of no pair of elements is a square. A well-known theorem of Furstenberg and Sarkozy states that D (n) = o (n). In the other direction, Ruzsa has proven that D (n) greater than or similar to n(gamma) for gamma = 1/2 (1 + log 7/log 65) approximate to 0.733077. We improve this to gamma = 1/2 (1 + log 7/log 65) approximate to 0.733412.

• 出版日期2015-2-16