Problem

Source: Mathcenter Contest / Oly - Thai Forum 2010 R1 p5 https://artofproblemsolving.com/community/c3196914_mathcenter_contest

Tags: number theory



The set $X$ of integers is called good If for each pair $a,b\in X$ , only one of $a+b,\mid a-b\mid$ is a member of $X$ ($a,b$ may be equal). Find the total number of sets with $2008$ as member. (tatari/nightmare)