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China Western Mathematical Olympiad
2024 China Western Mathematical Olympiad
2
2
Part of
2024 China Western Mathematical Olympiad
Problems
(1)
Integer sequence with bounds
Source: 2024 CWMO P2
8/6/2024
Find all integers
k
k
k
, such that there exists an integer sequence
{
a
n
}
{\{a_n\}}
{
a
n
}
satisfies two conditions below (1) For all positive integers
n
n
n
,
a
n
+
1
=
a
n
3
+
k
a
n
+
1
a_{n+1}={a_n}^3+ka_n+1
a
n
+
1
=
a
n
3
+
k
a
n
+
1
(2)
∣
a
n
∣
≤
M
|a_n| \leq M
∣
a
n
∣
≤
M
holds for some real
M
M
M
Sequence
algebra