Suppose we have $y[n+2]=y[n+1]+y[n]$ also known as fib sequence.
Then re-write it like: $y[n+2]-y[n+1]-y[n]= 0$ (Cool this is a homogeneous difference equation)
Now they claim that there exist a $r\in \mathbb R$ so that $y[n]=r^n$ . I agree with all of this concept but I do not understand why now $y[n+1]=r^n*r$
Actually I do not get how this idea of substitute working. Can someone explain to me??
I found it here: http://mathfaculty.fullerton.edu/mathews/c2003/ZTransformDEMod.html