# 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>. | ||

+ | |||

== Solution == | == Solution == | ||

+ | |||

+ | {{solution}} | ||

+ | |||

== See Also == | == See Also == | ||

− | *[[2006 USAMO Problems]] | + | |

+ | * [[2006 USAMO Problems]] | ||

+ | * [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=490647#p490647 Discussion on AoPS/MathLinks] | ||

+ | |||

+ | [[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

*This problem needs a solution. If you have a solution for it, please help us out by adding it.*