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2023 China TST Problem 17

Source: 2023 China TST Problem 17

March 29, 2023
algebracombinatoricsChina TST

Problem Statement

Whether there are integers a1a_1, a2a_2, ⋯\cdots, that are different from each other, satisfying: (1) For ∀k∈N+\forall k\in\mathbb N_+, ak2>0a_{k^2}>0 and ak2+k<0a_{k^2+k}<0; (2) For ∀n∈N+\forall n\in\mathbb N_+, ∣an+1−an∣⩽2023n\left| a_{n+1}-a_n\right|\leqslant 2023\sqrt n?
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