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?

Nice start, Jer.

One stray observation, which may or may not be useful, is that the left side of the equation = 0 (mod x-1)

This means that the right side also = 0 (mod x-1).

By casting out x-1's, this means that

(I + n + t + e + g + e + r) = 0 mod (x-1)