Product sets cannot contain long arithmetic progressions
Journal article, 2013

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, 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.

Convex sets

Product sets

Arithmetic progressions

Author

Dmitrii Zhelezov

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

Electronic Notes in Discrete Mathematics

1571-0653 (ISSN)

Vol. 43 169-170

Subject Categories

Mathematics

DOI

10.1016/j.endm.2013.07.028

More information

Created

10/7/2017