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Putnam
1993 Putnam
A2
A2
Part of
1993 Putnam
Problems
(1)
Putnam 1993 A2
Source: 1993 Putnam
10/26/2020
The sequence an of non-zero reals satisfies
a
n
2
−
a
n
−
1
a
n
+
1
=
1
a_n^2 - a_{n-1}a_{n+1} = 1
a
n
2
−
a
n
−
1
a
n
+
1
=
1
for
n
≥
1
n \geq 1
n
≥
1
. Prove that there exists a real number
α
\alpha
α
such that
a
n
+
1
=
α
a
n
−
a
n
−
1
a_{n+1} = \alpha a_n - a_{n-1}
a
n
+
1
=
α
a
n
−
a
n
−
1
for
n
≥
1
n \geq 1
n
≥
1
.
Putnam