Here is a problem I made up:

Let x belong to the set of integers.

That is, let x belong to the set containing the negative integers, zero, and the positive integers.

\(\displaystyle Let \ \ A \ = \ (x \ + \ (x - 1)\sqrt{x^2 - 1 \ } \ ), \ \ and \ \ let \ \ B \ = \ (-3x^2 - x + 4)\).

Imaginary numbers will be allowed for the \(\displaystyle \ \sqrt{x^2 - 1} \ \) expression.

**Solve \(\displaystyle \ A^B = 1, \ \ \) for all integer values of x only.**