## BdMO TST 2021 NT Exam P3 - For which $n$ does there exist a stable assignment?

- Anindya Biswas
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For an integer $n\geq3$ we consider a circle containing $n$ vertices. To each vertex we assign a positive integer, and these integers do not necessarily have to be distinct. Such an assignment of integers is called stable if the product of any three adjacent integers is $n$. For how many values of $n$ with $3\leq n\leq2020$ does there exist a stable assignment?

"If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is."

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**John von Neumann**