On Carmichael polynomials

Carmichael polynomials are introduced in polynomial ring F-q[t] which are analogues of Carmichael numbers in Z. We show that there exists infinitely many Carmichael polynomials for each q. Via higher Carlitz modules, we also have Carmichael polynomials of level n and we show that there exist infinitely many Carmichael polynomials of level n for each q and n. (C) 1998 Academic Press.