Difference between revisions of "2006 USAMO Problems/Problem 4"
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== Problem == | == Problem == | ||
| − | Find all positive integers <math>n</math> such that there are <math>k\ge 2</math> positive rational numbers <math>a_1,a_2,\ldots a_k</math> satisfying <math>a_1+a_2+...+a_k=a_1\cdot a_2\cdots a_k=n | + | |
| + | Find all positive integers <math> \displaystyle n</math> such that there are <math>k\ge 2</math> positive rational numbers <math>a_1,a_2,\ldots a_k</math> satisfying <math>a_1+a_2+...+a_k = a_1 \cdot a_2 \cdot \cdots a_k = n</math>. | ||
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== Solution == | == Solution == | ||
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| + | {{solution}} | ||
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== See Also == | == See Also == | ||
| − | *[[2006 USAMO Problems]] | + | |
| + | * [[2006 USAMO Problems]] | ||
| + | * [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=490647#p490647 Discussion on AoPS/MathLinks] | ||
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| + | [[Category:Olympiad Number Theory Problems]] | ||
Revision as of 19:43, 1 September 2006
Problem
Find all positive integers 
such that there are 
positive rational numbers 
satisfying 
.
Solution
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