# Decimal Expansion Buddies

$\frac{1}{271}=0.0036900369...$

$\frac{1}{369}=0.0027100271...$

If the decimal expansion of $$\frac{1}{a}$$ can be written as a string of $$5$$ digits repeated over and over ad infinitum, where the rightmost digits of the string form the number $$b$$ and any leading digits are $$0$$'s, (as per the example), then $$a$$ and $$b$$ are considered decimal expansion buddies.

How many distinct pairs of decimal expansion buddies are there?

Note: $$(a,b)$$ and $$(b,a)$$ are considered to be the same pair of numbers, and therefore are only counted once.

Bonus: Can you generalize this for any period length?

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