# How Many Good Pairs?

A pair of positive integers $$(m, n)$$ is called good if $$m$$ divides $$n^2+1$$ and $$n$$ divides $$m^2+1.$$

A positive integer $$n$$ is called admissible if there exists an integer $$m$$ for which the pair $$(m, n)$$ is good.

Find the sum of all admissible positive integers $$\leq 100.$$

Details and assumptions
- As an explicit example, since $$5$$ divides $$13^2+1$$ and $$13$$ divides $$5^2+1,$$ the pair $$(5, 13)$$ is good. This also implies $$5$$ are $$13$$ are admissible integers.
- This problem is an extension of an old BMO problem.

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