21 and 14 are divisible by 7 so let me reduce the expression to:
(3n + 4)/2n + 3).
Let n=1 and we have 7/6.
As we increase n we are going to generate instances of the given expression.
Excel is showing me that as n increases the quotient approaches 1.5.
Certainly not a proof.
An earlier comment was made about Russians and simplicity. I assume that was "tongue in cheek". I mean the IMO will have a difficulty range for the contestants.
I also assume that Ady may have acquired this via a Russian source since he has IMO in his text (International Mathematical Olympiad) see
http://www.imoofficial.org/problems.aspx for what might have been on offer for the past, and maybe some inspirations.

Posted by brianjn
on 20130330 02:29:18 