Lenstra′s Proof of the Carlitz-Wan Conjecture on Exceptional Polynomials: An Elementary Version

We give a proof, following an argument of Lenstra, of the conjecture of Carlitz (1966) as generalized by Wan (1993). This says that there are no exceptional polynomials of degree n over q if (n, q − 1) > 1. Fried, Guralnick, and Saxl previously proved Carlitz′s conjecture: there are no exceptional polynomials of even degree over fields of odd order.