Forty-eight irreducibility theorems (and still no thesis)
by
Robert F. Murphy
University of South Carolina

A polynomial f(x) is said to be reciprocal if f(x)= +/- x^degf f(1/x). The non-reciprocal part of f(x) is f(x) with its irreducible reciprocal factors removed. Selmer (1956) and Tverberg (1960) show that the non-reciprocal part of f(x)=xⁿ +/- x^a +/- 1 is irreducible (or +/- 1). Ljunggren (1960) and Mills (1985) show that the non-reciprocal part of f(x)=xⁿ +/- x^b +/- x^a +/- 1 is irreducible (or +/- 1) unless f(x) takes on certain specified forms. Filaseta and Solan recently obtained results for five and six-term polynomials with each coefficient equal to +1. We discuss a general algorithm for obtaining such results and classify all five and six-term polynomials with coefficients equal to +/- 1 whose non-reciprocal parts are reducible.

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Date received: April 16, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cacu-12.