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Omni-MATH / Let x₁,x₂,…,x₂₀₂₂ be nonzero real numbers. Suppose that x_(k)+(1)/(x_(k+1))<0 for each 1≤k≤2022, where x₂₀₂₃=x₁. Compute the maximum possible number of integers 1≤n≤2022 such that …

Problem

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problem

Let x1,x2,…,x2022x_{1}, x_{2}, \ldots, 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.
Plain-text mathematical notation (without MathML)
Let x₁,x₂,…,x₂₀₂₂ be nonzero real numbers. Suppose that x_(k)+(1)/(x_(k+1))<0 for each 1≤k≤2022, where x₂₀₂₃=x₁. Compute the maximum possible number of integers 1≤n≤2022 such that x_(n)>0.
Original LaTeX notation
Let $x_{1}, x_{2}, \ldots, x_{2022}$ be nonzero real numbers. Suppose that $x_{k}+\frac{1}{x_{k+1}}<0$ for each $1 \leq k \leq 2022$, where $x_{2023}=x_{1}$. Compute the maximum possible number of integers $1 \leq n \leq 2022$ such that $x_{n}>0$.

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Source and history

task_id
60cb506b-042c-544d-b8f8-78ef810fda69
task_key
test--60cb506b-042c-544d-b8f8-78ef810fda69
task_revision_id
1
config / split
/ test

Official source

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