The Cauchy-Mirimanoff Polynomials are a class of polynomials that naturally arise in various classical studies of Fermat's Last Theorem. Originally conjectured to be irreducible over 100 years ago, the irreducibility of the Cauchy-Mirimanoff polynomials is still an open conjecture.
This dissertation takes a new approach to the study of the Cauchy-Mirimanoff Polynomials. The reciprocal transform of a self-reciprocal polynomial is defined, and the reciprocal transforms of the Cauchy-Mirimanoff Polynomials are found and studied. Particular attention is given to the Cauchy-Mirimanoff Polynomials with index three times a power of a prime, and it is shown that the Cauchy-Mirimanoff Polynomials of index three times a prime are irreducible.
Identifer | oai:union.ndltd.org:UTENN/oai:trace.tennessee.edu:utk_graddiss-1730 |
Date | 01 May 2010 |
Creators | Irick, Brian C |
Publisher | Trace: Tennessee Research and Creative Exchange |
Source Sets | University of Tennessee Libraries |
Detected Language | English |
Type | text |
Format | application/pdf |
Source | Doctoral Dissertations |
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