IMO Shortlist 1984 problem 6


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2. travnja 2012.
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Let c be a positive integer. The sequence \{f_n\} is defined as follows:
f_1 = 1, f_2 = c, f_{n+1} = 2f_n - f_{n-1} + 2 \quad  (n \geq 2).
Show that for each k \in \mathbb N there exists r \in \mathbb N such that f_kf_{k+1}= f_r.
Izvor: Međunarodna matematička olimpijada, shortlist 1984