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Difference between numbers of elements in A-A and A+A

Source: Schweitzer 2009

November 13, 2009

searchlimitset theorycombinatorics proposedcombinatorics

Problem Statement

Prove that there exist positive constants

c

and

n_0

with the following property. If

A

is a finite set of integers, |A| \equal{} n > n_0, then |A \minus{} A| \minus{} |A \plus{} A| \leq n^2 \minus{} c n^{8/5}.