A mapping f: GF(pⁿ)→GF(pⁿ) is called differentially k-uniform if k is the maximum number of solutions x∊GF(pⁿ) of f(x+a)−f(x)=b, where a,b∊GF(pⁿ) and a≠0. A 1-uniform mapping is called perfect nonlinear (PN). In this paper we discuss some problems related to the equivalence of perfect nonlinear functions, and describe a class of perfect nonlinear binomials ux^pk+1+x² in GF(p^2k). These are the first PN binomials known to us which are composed with inequivalent monomials. We show that this family of binomials is equivalent to the monomial x². We survey some of the close connections between perfect nonlinear functions and finite affine planes, in particular those which are important for equivalence proofs.