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CAUCHY–MIRIMANOFF AND RELATED POLYNOMIALS

Part of: Polynomials and matrices

Published online by Cambridge University Press:  27 September 2012

PAUL M. NANNINGA
PAUL M. NANNINGA*
Affiliation:
Centre for Mathematics and its Applications, Mathematical Sciences Institute, Australian National University, Canberra, ACT 0200, Australia (email: paul.nanninga@anu.edu.au)
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Abstract

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In 1903 Mirimanoff conjectured that Cauchy–Mirimanoff polynomials En are irreducible over ℚ for odd prime n. Polynomials Rn, Sn, Tn are introduced, closely related to En. It is proved that Rm, Sm, Tm are irreducible over ℚ for odd m≥3 , and En, Rn, Sn are irreducible over ℚ, for n=2qm, q=1,2,3,4,5 , and m≥1 odd.

Keywords

irreducible polynomialsCauchy–Mirimanoff polynomialFermat’s last theorem

MSC classification

Secondary: 11C08: Polynomials
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 92 , Issue 2 , April 2012 , pp. 269 - 280
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2012

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