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1986 IMO Longlists
64
a_n is perfect square for every n
a_n is perfect square for every n
Source:
August 29, 2010
induction
number theory unsolved
number theory
Problem Statement
Let
(
a
n
)
n
∈
N
(a_n)_{n\in \mathbb N}
(
a
n
)
n
∈
N
be the sequence of integers defined recursively by
a
1
=
a
2
=
1
,
a
n
+
2
=
7
a
n
+
1
−
a
n
−
2
a_1 = a_2 = 1, a_{n+2} = 7a_{n+1} - a_n - 2
a
1
=
a
2
=
1
,
a
n
+
2
=
7
a
n
+
1
−
a
n
−
2
for
n
≥
1
n \geq 1
n
≥
1
. Prove that
a
n
a_n
a
n
is a perfect square for every
n
.
n.
n
.
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