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Czech-Polish-Slovak Match
2006 Czech-Polish-Slovak Match
5
5
Part of
2006 Czech-Polish-Slovak Match
Problems
(1)
A sequence that remains integral
Source: Czech-Polish-Slovak 2006 Q5
4/27/2013
Find the number of sequences
(
a
n
)
n
=
1
∞
(a_n)_{n=1}^\infty
(
a
n
)
n
=
1
∞
of integers satisfying
a
n
≠
−
1
a_n \ne -1
a
n
=
−
1
and
a
n
+
2
=
a
n
+
2006
a
n
+
1
+
1
a_{n+2} =\frac{a_n + 2006}{a_{n+1} + 1}
a
n
+
2
=
a
n
+
1
+
1
a
n
+
2006
for each
n
∈
N
n \in \mathbb{N}
n
∈
N
.
calculus
integration
algebra unsolved
algebra