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Putnam 2005 B2

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December 5, 2005
Putnaminequalitiescollege contests

Problem Statement

Find all positive integers n,k1,…,knn,k_1,\dots,k_n such that k1+⋯+kn=5n−4k_1+\cdots+k_n=5n-4 and 1k1+⋯+1kn=1. \frac1{k_1}+\cdots+\frac1{k_n}=1.
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