Let p be an odd prime with A, d positive integers satisfying (d, p-1)=1 and p not dividing A. We would like to know when the map from Z\pZ to Z\pZ sending x to Ax^d permutes the even residues (0, 2, 4, ..., p-1) mod p. Goresky and Klapper conjecture that for p > 13 this map permutes the even residues only when A=d=1. This conjecture arises from an equivalent conjecture about a class of binary sequences called l-sequences. We will talk about how to use binomial sum bounds to prove the Goresky-Klapper conjecture for any prime p > 2.26 x 10^55.