n is a positive integer base from 2 to 36 inclusively.
Each of α and β is a nonzero digit of base n from 1 to n-1 inclusively.

Determine all possible triplets (α, β, n) such that:

(α*β)base n
-----------  is a positive integer.
(α.β)base n 

### For example, in base ten corresponding to (α, β) = (4, 5), we observe that:
(4*5)/(4.5) = 40/9, which is NOT a positive integer.