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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.