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The Incongruence of Consecutive Values of Polynomials

✍ Scribed by Pieter Moree

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
325 KB
Volume
2
Category
Article
ISSN
1071-5797

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✦ Synopsis

Suppose that f Κ¦ β€«Ν‰ήšβ€¬xΝ‰. Put D f (n) Ο­ minΝ•k ΟΎ 0 Ν‰ f (1), . . . , f (n) are pairwise incongruent modulo kΝ–. 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 all f in a large subset of β€«Ν‰ήšβ€¬xΝ‰ provides a characterization of D f (n) for all n sufficiently large. This theorem partially encompasses results due to Bremser, Schumer and Washington and to Moree and Mullen, who characterized D f (n) for cyclic, respectively, Dickson polynomials.

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