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irreducible? (Posted on 2013-03-29) Difficulty: 2 of 5
Prove that the fraction (21n+4)/(14n+3) is irreducible for every natural number n.

Source: Russian IMO

No Solution Yet Submitted by Ady TZIDON    
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An Observation and a Russian Note | Comment 4 of 6 |
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 for what might have been on offer for the past, and maybe some inspirations.

  Posted by brianjn on 2013-03-30 02:29:18
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