Electronic Notes in Discrete MathematicsVolume 43, 5 September 2013, Pages 169-170Product sets cannot contain long arithmetic progressionsAuthor links open overlay panelDmitry ZhelezovShow moreShareCitehttps://doi.org/10.1016/j.endm.2013.07.028Get rights and contentAbstractLet 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,bj∈B} 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.Recommended articlesReferences (2)J. SolymosiBounding multiplicative energy by the sumsetAdv. Math.(2009)P. Erdős et al.Sums and products of integers(1983)Cited by (0)View full textCopyright © 2013 Elsevier B.V. All rights reserved.