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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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Hints/Tips re(2): hmmmm finding limit Comment 6 of 6 |
(In reply to re: hmmmm by brianjn)

Brian,

The limit is, as you have rightly observed , but to orove it you do not need simulation or Excel tables.

You divide both the numerator  and the denominator by n:

(21+4/n)/(14+3/n)  and let nšinfinity 
the fraction is 21/14=1/3.

Generally the limit of a ratio of 2 polynomes of a single variable=

a. }infinity, (higher power polynome in the numerator)

b, zero (lower power polynome in the numerator)

    or

c, ratio of the highest power's coefficients(equal powers).


  Posted by Ady TZIDON on 2013-03-31 08:06:34
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