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Problems
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National and Regional Contests
PEN Problems
PEN M Problems
28
28
Part of
PEN M Problems
Problems
(1)
M 28
Source:
5/25/2007
Let
{
u
n
}
n
≥
0
\{u_{n}\}_{n \ge 0}
{
u
n
}
n
≥
0
be a sequence of integers satisfying the recurrence relation
u
n
+
2
=
u
n
+
1
2
−
u
n
u_{n+2}=u_{n+1}^2 -u_{n}
u
n
+
2
=
u
n
+
1
2
−
u
n
(
n
∈
N
)
(n \in \mathbb{N})
(
n
∈
N
)
. Suppose that
u
0
=
39
u_{0}=39
u
0
=
39
and
u
1
=
45
u_{1}=45
u
1
=
45
. Prove that
1986
1986
1986
divides infinitely many terms of this sequence.
Recursive Sequences