complicated cas problem

[webmasterpdx]

I have 2 functions. The first is a staircase function:

f1=atan(cot(pi*x))/pi + x - 1/2

The second is basically, fermats equation...x^n + y^n = z^n
I can prove it only needs to be true in the positive domain....so I can use:
y = f2 = (z^n - x^n)^(1/n)
If n = 2, this is a circle.

So, I wanted to see where these 2 functions intersect as in:
f1(x) = f2(x)

I tried:

solve(f1(x) = f2(x),{x,y}) and I only get an empty square brackets (matrix) as a result.

Then I tried n:=2, and it tells me I have a bad argument.
I tried z:=5 and I get the same result.

How do I get the intersection of 2 functions like this algebraicly.

I know when I plot these functions with the values of z and n above, that (x,y) = (4,3) is a result....when I look at the plots....so it should be easy to solve.

???