1. The problem statement, all variables and given/known data Prove that there exists two infinite sequences <an> and <bn> of positive integers such that the following conditions hold simultaneously: i) 1<a1<a2<a3.......; ii) an<bn<(an)^2 for all n>=1 iii)(an) - 1 divides (bn) - 1 for all n>=1 iv)(an)^2 -1 divides (bn)^2 - 1 for all n>=1 2. Relevant equations 3. The attempt at a solution What I guess from this question is that both the series must be odd. Am I right? From iii) an iv) I deduce that bn+1 |mod| an+1 =0 for n>=1 Please help me further!!!!