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1983 IMO Longlists
30
Prove that there exist a unique sequence
Prove that there exist a unique sequence
Source:
October 5, 2010
algebra unsolved
algebra
Problem Statement
Prove the existence of a unique sequence
{
u
n
}
(
n
=
0
,
1
,
2
…
)
\{u_n\} \ (n = 0, 1, 2 \ldots )
{
u
n
}
(
n
=
0
,
1
,
2
…
)
of positive integers such that
u
n
2
=
∑
r
=
0
n
(
n
+
r
r
)
u
n
−
r
for all
n
≥
0
u_n^2 = \sum_{r=0}^n \binom{n+r}{r} u_{n-r} \qquad \text{for all } n \geq 0
u
n
2
=
r
=
0
∑
n
(
r
n
+
r
)
u
n
−
r
for all
n
≥
0
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