Elsevier

Electronic Notes in Discrete Mathematics

Volume 43, 5 September 2013, Pages 169-170
Electronic Notes in Discrete Mathematics

Product sets cannot contain long arithmetic progressions

https://doi.org/10.1016/j.endm.2013.07.028Get rights and content

Abstract

Let B be a set of real numbers of size n. We prove that the length of the longest arithmetic progression contained in the product set B.B={bibj|bi,bjB} cannot be greater than O(n1+1/loglogn) an arithmetic progression of length Ω(nlogn), so the obtained upper bound is close to the optimal.

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