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China Team Selection Test
2023 China Team Selection Test
P17
P17
Part of
2023 China Team Selection Test
Problems
(1)
2023 China TST Problem 17
Source: 2023 China TST Problem 17
3/29/2023
Whether there are integers
a
1
a_1
a
1
,
a
2
a_2
a
2
,
⋯
\cdots
⋯
, that are different from each other, satisfying: (1) For
∀
k
∈
N
+
\forall k\in\mathbb N_+
∀
k
∈
N
+
,
a
k
2
>
0
a_{k^2}>0
a
k
2
>
0
and
a
k
2
+
k
<
0
a_{k^2+k}<0
a
k
2
+
k
<
0
; (2) For
∀
n
∈
N
+
\forall n\in\mathbb N_+
∀
n
∈
N
+
,
∣
a
n
+
1
−
a
n
∣
⩽
2023
n
\left| a_{n+1}-a_n\right|\leqslant 2023\sqrt n
∣
a
n
+
1
−
a
n
∣
⩽
2023
n
?
algebra
combinatorics
China TST