Each of the small letters in bold represents a different base x digit from 0 to x-1 to satisfy this alphametic equation. None of the numbers can contain any leading zero.

(x-1)***number** = **integer**

Determine the minimum positive integer value of x such that the above equation has at least one solution. What is the next smallest value of x having this property?

(In reply to

Parametric solutions by Brian Smith)

Let z=x/2. Then a parametric solution for all even bases starting with x=14 is:

B=z-2, E=z, G=1, I=2z-4, M=2z-2, N=2z-3, R=0, T=3, U=2z-6

2z-4 2z-3 3 z 1 z 0

+ 2z-3 2z-6 2z-2 z-2 z 0

---------------------------

2z-3 2z-6 2z-2 z-2 z 0 0