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Existence of sequences

  1. Nov 9, 2008 #1
    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

    From iii) an iv) I deduce that bn+1 |mod| an+1 =0 for n>=1

    Please help me further!!!!
  2. jcsd
  3. Nov 9, 2008 #2
    Re: Cubic Equations

    I am very sorry I keyed in the wrong title for the post! MODS if you could please change it to Sequences?
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