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Baltic Way
2021 Baltic Way
3
3
Part of
2021 Baltic Way
Problems
(1)
Infinite sequence on positives
Source: Baltic Way 2021, Problem 3
11/15/2021
Determine all infinite sequences
(
a
1
,
a
2
,
…
)
(a_1,a_2,\dots)
(
a
1
,
a
2
,
…
)
of positive integers satisfying
a
n
+
1
2
=
1
+
(
n
+
2021
)
a
n
a_{n+1}^2=1+(n+2021)a_n
a
n
+
1
2
=
1
+
(
n
+
2021
)
a
n
for all
n
≥
1
n \ge 1
n
≥
1
.
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Baltic Way