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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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re: hmmmm | Comment 3 of 6 |
(In reply to hmmmm by broll)

Well, if your point is that this problem is easy for a Russian IMO, I must agree.

However, I don't understand your proof.

For instance,
(3n - 2)/(2n) = 3/2 - 1/n, but that doesn't make (3n - 2)/(2n) irreducible.  In fact,  (3n - 2)/(2n) is reducible for all even n.

  Posted by Steve Herman on 2013-03-29 18:33:20
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