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National and Regional Contests
PEN Problems
PEN N Problems
5
N 5
N 5
Source:
May 25, 2007
More Sequences
Problem Statement
Prove that there exist two strictly increasing sequences
a
n
a_{n}
a
n
and
b
n
b_{n}
b
n
such that
a
n
(
a
n
+
1
)
a_{n}(a_{n} +1)
a
n
(
a
n
+
1
)
divides
b
n
2
+
1
b_{n}^2 +1
b
n
2
+
1
for every natural
n
n
n
.
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