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)### For example, in base ten corresponding to (α, β) = (4, 5), we observe that:_{base n}----------- is a positive integer. (α.β)_{base n}

(4*5)/(4.5) = 40/9, which is NOT a positive integer.