How Many Ways to Place Divisors Around a Circle in Mathematical Induction?

AI Thread Summary
The discussion centers on the problem of determining the number of ways to arrange divisors of a natural number N around a circle, ensuring that each number is a divisor of the sum of its two adjacent numbers. Clarification is sought regarding the constraints on N, particularly the need to specify that the numbers placed must be less than or equal to N. The relationship to mathematical induction is mentioned, suggesting that this approach may be relevant to solving the problem. Participants express the need for clearer definitions and constraints to facilitate a proper analysis. The conversation highlights the importance of precise mathematical conditions in combinatorial problems.
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I want to now the answer of this question and I think it relates to mathematical induction. The question is:
-Suppose is a natural number. In how many ways can we place numbers around a circle such that each number is a divisor of the sum of it's two adjacent numbers?

Who can answer this question?
 
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You seem to have omitted some words. Suppose N is a natural number? Then you need some constraint based on N, such as "place numbers <= N around a circle".
 

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