1arey this came today in RMO naa????
Prove that there exist two infinite sequences (an)n≥1 and (bn)n≥1 of positive integers such that the following conditions hold simultaneously:
(i) 1 < a1 < a2 < a3 ....
(ii) an<bn<a2n, for all n ≥1
(iii)an-1 is divides bn-1, for all n≥1;
(iv)a2n-1 divides b2n-1, for all n≥1
I am really sorry , had to edit 1 part -
(iii) made it to bn-1 from bn
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