Differentially Uniform

Given \( \delta \in \Z^+ \), we call an \( (m,n,p) \)-function differentially \(\delta\)-uniform if for every nonzero \( a \in \mathbb{F}_{p^m} \), and for every \( b \in \mathbb{F}_{p^n} \), the difference equation: \[ D_a{f(x)}=b \] has at most \(\delta\)-solutions.