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Sequence of positive integers

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September 8, 2010
algebraSequencerecurrence relationLinear RecurrencesIMO Shortlist

Problem Statement

Let cc be a positive integer. The sequence {fn}\{f_n\} is defined as follows: f_1 = 1, f_2 = c, f_{n+1} = 2f_n - f_{n-1} + 2   (n \geq 2). Show that for each k∈Nk \in \mathbb N there exists r∈Nr \in \mathbb N such that fkfk+1=fr.f_kf_{k+1}= f_r.
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