Problem D

The Same Power

Sometimes two powers that are not written with the same base are still equal in value. For example, \(9^3 = 27^2\) and \((-5)^4=25^2\).

If \(x\) and \(y\) are integers, find all ordered pairs \((x,y)\) that satisfy the equation \[(x-1)^{x+y}=8^2\]