Difference between revisions of "2021 USAJMO Problems/Problem 6"

Problem

Let $n \geq 4$ be an integer. Find all positive real solutions to the following system of $2n$ equations:\begin{align*} a_{1} &=\frac{1}{a_{2 n}}+\frac{1}{a_{2}}, & a_{2}&=a_{1}+a_{3}, \\ a_{3}&=\frac{1}{a_{2}}+\frac{1}{a_{4}}, & a_{4}&=a_{3}+a_{5}, \\ a_{5}&=\frac{1}{a_{4}}+\frac{1}{a_{6}}, & a_{6}&=a_{5}+a_{7}, \\ &\vdots \\ a_{2 n-1}&=\frac{1}{a_{2 n-2}}+\frac{1}{a_{2 n}}, & a_{2 n}&=a_{2 n-1}+a_{1} \end{align*}

See Also

 2021 USAJMO (Problems • Resources) Preceded byProblem 4 Followed byLast Problem 1 • 2 • 3 • 4 • 5 • 6 All USAJMO Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.

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