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2023 Thailand Online MO
9
(n^2+1)a_n=n(a_{n^2}+1)
(n^2+1)a_n=n(a_{n^2}+1)
Source: 2023 Thailand Online MO P9
February 12, 2023
number theory
Integer sequence
algebra
Problem Statement
Find all sequences of positive integers
a
1
,
a
2
,
…
a_1,a_2,\dots
a
1
,
a
2
,
…
such that
(
n
2
+
1
)
a
n
=
n
(
a
n
2
+
1
)
(n^2+1)a_n = n(a_{n^2}+1)
(
n
2
+
1
)
a
n
=
n
(
a
n
2
+
1
)
for all positive integers
n
n
n
.
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