Abstract
Suppose thatf∈ Z|x|. PutDf(n) = min{k> 0|f(1), ... ,f(n) are pairwise incongruent modulok}. Special cases of this function were previously considered, using methods from elementary number theory. Results from the theory of finite fields are used to prove a theorem that for allfin a large subset of Z|x| provides a characterization ofDf(n) for allnsufficiently large. This theorem partially encompasses results due to Bremser, Schumer and Washington and to Moree and Mullen, who characterizedDf(n) for cyclic, respectively, Dickson polynomials.
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