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2022 Algebra/NT #3

Source:

March 11, 2022
algebra

Problem Statement

Let x1,x2,...,x2022x_1, x_2, . . . , x_{2022} be nonzero real numbers. Suppose that xk+1xk+1<0x_k + \frac{1}{x_{k+1}} < 0 for each 1≤k≤20221 \leq k \leq 2022, where x2023=x1x_{2023}=x_1. Compute the maximum possible number of integers 1≤n≤20221 \leq n \leq 2022 such that xn>0x_n > 0.
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