Difference between revisions of "2005 USAMO Problems"
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* [http://www.unl.edu/amc/e-exams/e8-usamo/e8-1-usamoarchive/2006-ua/2006usamoS.pdf 2005 USAMO Solutions] | * [http://www.unl.edu/amc/e-exams/e8-usamo/e8-1-usamoarchive/2006-ua/2006usamoS.pdf 2005 USAMO Solutions] | ||
* [http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=27&year=2005 USAMO Problems on the Resources page] | * [http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=27&year=2005 USAMO Problems on the Resources page] | ||
− | {{USAMO newbox|year= | + | {{USAMO newbox|year=2005|before=[[2004 USAMO]]|after=2006 USAMO}} |
Revision as of 13:27, 3 May 2008
Contents
Day 1
Problem 1
Determine all composite positive integers for which it is possible to arrange all divisors of that are greater than 1 in a circle so that no two adjacent divisors are relatively prime.
Problem 2
Prove that the system has no solutions in integers , , and .
Problem 3
Let be an acute-angled triangle, and let and be two points on side . Construct point in such a way that convex quadrilateral is cyclic, , and and lie on opposite sides of line . Construct point in such a way that convex quadrilateral is cyclic, , and and lie on opposite sides of line . Prove that points , and lie on a circle.
Day 2
Problem 4
This problem needs a solution. If you have a solution for it, please help us out by adding it.
Problem 5
This problem needs a solution. If you have a solution for it, please help us out by adding it.
Problem 6
This problem needs a solution. If you have a solution for it, please help us out by adding it.
Resources
- USAMO Problems and Solutions
- 2005 USAMO Problems
- 2005 USAMO Solutions
- USAMO Problems on the Resources page
2005 USAMO (Problems • Resources) | ||
Preceded by 2004 USAMO |
Followed by 2006 USAMO | |
1 • 2 • 3 • 4 • 5 • 6 | ||
All USAMO Problems and Solutions |