A polygon with $1997$ vertices is given. Write a positive real number each vertex such that, each number equal to its right and left numbers' arithmetic or geometric mean. Prove that all numbers are equal.
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Tags: polygon, combinatorics
A polygon with $1997$ vertices is given. Write a positive real number each vertex such that, each number equal to its right and left numbers' arithmetic or geometric mean. Prove that all numbers are equal.
