Abstract :
Carmichael polynomials are introduced in polynomial ring imageq[t] which are analogues of Carmichael numbers in image. We show that there exists infinitely many Carmichael polynomials for eachq. Via higher Carlitz modules, we also have Carmichael polynomials of levelnand we show that there exist infinitely many Carmichael polynomials of levelnfor eachqandn.
