Is this a pseudo random function (PRF)? F(k,x) = f(k,x) - f(k,x-1) I have a question about Pseudo Random Functions.

Let $f:\{0,1\}^m \times \{0,1\}^n → \{0,1\}^n$ be a secure PRF.

Define $F(k,x) = f(k,x) - f(k, x-1 \bmod 2^{n}) \bmod 2^{n}$.

Is $F$ is a secure PRF?
Not if the attacker is given enough time to ask for the values $F(k,x)$ for all $2^n$ values of $x$.  We have

$\Sigma_x F(k,x) = 0$

which is distinguishable from random.