IMO Shortlist 2001 problem A5


Kvaliteta:
  Avg: 0,0
Težina:
  Avg: 8,0
Dodao/la: arhiva
2. travnja 2012.
LaTeX PDF
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.
Izvor: Međunarodna matematička olimpijada, shortlist 2001