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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 http://www.imo-official.org/problems.aspx 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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