Difference between revisions of "2005 USAMO Problems/Problem 1"

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== Problem ==
 
== Problem ==
 
 
Determine all composite positive integers <math>n</math> for which it is possible to arrange all divisors of <math>n</math> that are greater than 1 in a circle so that no two adjacent divisors are relatively prime.
 
Determine all composite positive integers <math>n</math> for which it is possible to arrange all divisors of <math>n</math> that are greater than 1 in a circle so that no two adjacent divisors are relatively prime.
  
 
== Solution ==
 
== Solution ==
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{{solution}}
  
 
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== See also ==
{{alternate solutions}}
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{{USAMO newbox|year=2005|before=First Question|num-a=2}}
 
 
== Resources ==
 
 
 
{{USAMO newbox|year=2005|before=First question|num-a=2}}
 
 
 
  
 
[[Category:Olympiad Number Theory Problems]]
 
[[Category:Olympiad Number Theory Problems]]

Revision as of 13:04, 3 May 2008

Problem

Determine all composite positive integers $n$ for which it is possible to arrange all divisors of $n$ that are greater than 1 in a circle so that no two adjacent divisors are relatively prime.

Solution

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See also

2005 USAMO (ProblemsResources)
Preceded by
First Question
Followed by
Problem 2
1 2 3 4 5 6
All USAMO Problems and Solutions
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