Difference between revisions of "1959 IMO Problems/Problem 1"

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== Problem ==
 
== Problem ==
  
Prove that the fraction <math>\frac{21n+4}{14+3}</math> is irreducible for every natural number <math>\displaystyle n</math>.
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Prove that the fraction <math>\frac{21n+4}{14n+3}</math> is irreducible for every natural number <math>\displaystyle n</math>.
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== Solution ==
 
== Solution ==
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and we're done.
 
and we're done.
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== Resources ==
 
== Resources ==

Revision as of 18:32, 25 July 2006

Problem

Prove that the fraction $\frac{21n+4}{14n+3}$ is irreducible for every natural number $\displaystyle n$.


Solution

We observe that

$\displaystyle 3(14n+3) = 2(21n+4) + 1,$

and we're done.


Resources