Problem

Source: 2023 China TST Problem 17

Tags: algebra, combinatorics, China TST



Whether there are integers $a_1$, $a_2$, $\cdots$, that are different from each other, satisfying: (1) For $\forall k\in\mathbb N_+$, $a_{k^2}>0$ and $a_{k^2+k}<0$; (2) For $\forall n\in\mathbb N_+$, $\left| a_{n+1}-a_n\right|\leqslant 2023\sqrt n$?