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2001 IMO Shortlist Problems/A5

Revision as of 18:16, 20 August 2008 by Minsoens (talk | contribs) (New page: == Problem == Find all positive integers <math>a_1, a_2, \ldots, a_n</math> such that <center><math>\frac {99}{100} = \frac {a_0}{a_1} + \frac {a_1}{a_2} + \cdots + \frac {a_{n - 1}}{a_n},...)

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Problem

Find all positive integers $a_1, a_2, \ldots, a_n$ such that

$\frac {99}{100} = \frac {a_0}{a_1} + \frac {a_1}{a_2} + \cdots + \frac {a_{n - 1}}{a_n},$

where $a_0 = 1$ and $(a_{k + 1} - 1)a_{k - 1} \geq a_k^2(a_k - 1)$ for $k = 1,2,\ldots,n - 1$ .

Solution

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