(adsbygoogle = window.adsbygoogle || []).push({}); 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!!!!

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# Homework Help: Existence of sequences

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