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Omni-MATH / Let n≥2 be an integer. Find all real numbers a such that there exist real numbers x₁, …,x_(n) satisfying x₁(1−x₂)=x₂(1−x₃)=…=x_(n−1)(1−x_(n))=x_(n)(1−x₁)=a

Problem

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problem

Let n≥2n \geq 2 be an integer. Find all real numbers aa such that there exist real numbers x1x_{1}, …,xn\ldots, x_{n} satisfying x1(1−x2)=x2(1−x3)=…=xn−1(1−xn)=xn(1−x1)=ax_{1}\left(1-x_{2}\right)=x_{2}\left(1-x_{3}\right)=\ldots=x_{n-1}\left(1-x_{n}\right)=x_{n}\left(1-x_{1}\right)=a
Plain-text mathematical notation (without MathML)
Let n≥2 be an integer. Find all real numbers a such that there exist real numbers x₁, …,x_(n) satisfying x₁(1−x₂)=x₂(1−x₃)=…=x_(n−1)(1−x_(n))=x_(n)(1−x₁)=a
Original LaTeX notation
Let $n \geq 2$ be an integer. Find all real numbers $a$ such that there exist real numbers $x_{1}$, $\ldots, x_{n}$ satisfying $$x_{1}\left(1-x_{2}\right)=x_{2}\left(1-x_{3}\right)=\ldots=x_{n-1}\left(1-x_{n}\right)=x_{n}\left(1-x_{1}\right)=a$$

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Source and history

task_id
c423f4bc-dab7-5d40-98be-3b06a8f67304
task_key
test--c423f4bc-dab7-5d40-98be-3b06a8f67304
task_revision_id
1
config / split
/ test

Official source

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