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Putnam
1980 Putnam
B3
Putnam 1980 B3
Putnam 1980 B3
Source: Putnam 1980
April 1, 2022
Putnam
Sequences
Problem Statement
For which real numbers
a
a
a
does the sequence
(
u
n
)
(u_n )
(
u
n
)
defined by the initial condition
u
0
=
a
u_0 =a
u
0
=
a
and the recursion
u
n
+
1
=
2
u
n
−
n
2
u_{n+1} =2u_n - n^2
u
n
+
1
=
2
u
n
−
n
2
have
u
n
>
0
u_n >0
u
n
>
0
for all
n
≥
0
?
n \geq 0?
n
≥
0
?
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