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.</math>
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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]]
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* [[2006 USAMO Problems]]
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* [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 $\displaystyle n$ such that there are $k\ge 2$ positive rational numbers $a_1,a_2,\ldots a_k$ satisfying $a_1+a_2+...+a_k = a_1 \cdot a_2 \cdot \cdots a_k = n$.

Solution

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See Also

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