On Carmichael Polynomials

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Abstract

Carmichael polynomials are introduced in polynomial ring Fq[t] which are analogues of Carmichael numbers in Z. 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.

Original languageEnglish
Pages (from-to)257-274
Number of pages18
JournalJournal of Number Theory
Volume71
Issue number2
DOIs
Publication statusPublished - 1998 Aug 1

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ASJC Scopus subject areas

  • Algebra and Number Theory

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