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

[Thoughful]

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?

 

[haruspex]

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".