On A Conjecture of Conway

Abstract

Problem 7 of Section VI of H. T. Croft's "Research Problems" (August, 1967 edition) is by J. H. Conway:A is a finite set of integers {ai}. A + A denotes {ai + aj}, A - A denotes {ai - aj}. Prove that A - A always has more members than A + A, unless A is symmetrical about 0.First note that 'about 0' is redundant and erroneous.