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A sequence that remains integral

Source: Czech-Polish-Slovak 2006 Q5

April 27, 2013

calculusintegrationalgebra unsolvedalgebra

Problem Statement

Find the number of sequences

(a_n)_{n=1}^\infty

of integers satisfying

a_n \ne -1

and

a_{n+2} =\frac{a_n + 2006}{a_{n+1} + 1}

for each

n \in \mathbb{N}

.

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