Product sets cannot contain long arithmetic progressions
Journal article, 2014

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}B.B={bibj|bi,bj∈B} cannot be greater than View the MathML sourceO(n1+1/loglogn) an arithmetic progression of length View the MathML sourceΩ(nlogn), so the obtained upper bound is close to the optimal.

arithmetic progressions

product sets

convex sets

Author

Dmitrii Zhelezov

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

Acta Arithmetica

0065-1036 (ISSN)

Vol. 163 4 299-307

Roots

Basic sciences

Subject Categories

Discrete Mathematics

DOI

10.4064/aa163-4-1

More information

Created

10/7/2017