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Flanders Math Olympiad
1986 Flanders Math Olympiad
3
[solved] - easy sequence
[solved] - easy sequence
Source: first flanders olympiad, '86
August 9, 2004
number theory proposed
number theory
Problem Statement
Let
{
a
k
}
k
≥
0
\{a_k\}_{k\geq 0}
{
a
k
}
k
≥
0
be a sequence given by
a
0
=
0
a_0 = 0
a
0
=
0
,
a
k
+
1
=
3
⋅
a
k
+
1
a_{k+1}=3\cdot a_k+1
a
k
+
1
=
3
⋅
a
k
+
1
for
k
∈
N
k\in \mathbb{N}
k
∈
N
. Prove that
11
∣
a
155
11 \mid a_{155}
11
∣
a
155
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