I am currently investigating the correlation between a natural number and the length of its inverse’s period. For example:

$$

frac{1}{3760} = 0.00026595744680851063829787234042553191489361702127 (period 46) \

frac{1}{1122} = 0.00089126559714795 (period 16)

$$

And so on.

There is a simple explanation for why does this happen mixing powers and modular arithmetic but it’s just an iterative process, which is troublesome for really big numbers.

`Which conjectures, theories, hypothesis exists regarding the computation of the periodic length of any natural number's inverse?`