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Moldova Contests
JBMO TST - Moldova
2019 Junior Balkan Team Selection Tests - Moldova
2
Moldova JTST 2019 P2
Moldova JTST 2019 P2
Source:
April 19, 2019
combinatorics
Problem Statement
The numeric sequence
(
a
n
)
n
≥
1
(a_n)_{n\geq1}
(
a
n
)
n
≥
1
verifies the relation
a
n
+
1
=
n
+
2
n
⋅
(
a
n
−
1
)
a_{n+1} = \frac{n+2}{n} \cdot (a_n-1)
a
n
+
1
=
n
n
+
2
⋅
(
a
n
−
1
)
for any
n
∈
N
∗
n\in N^*
n
∈
N
∗
.Show that
a
n
∈
Z
a_n \in Z
a
n
∈
Z
for any
n
∈
N
∗
n\in N^*
n
∈
N
∗
,if
a
1
∈
Z
a_1\in Z
a
1
∈
Z
.
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