Cauchy"mirimanoff and related polynomials

Paul M. Nanninga

doi:10.1017/S1446788712000195

Cauchy"mirimanoff and related polynomials

Paul M. Nanninga^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

Abstract In 1903 Mirimanoff conjectured that Cauchy"Mirimanoff polynomials E n are irreducible over â.,š for odd prime n. Polynomials R n, S n, T n are introduced, closely related to E n. It is proved that R m, S m, T m are irreducible over â.,š for odd mâ‰13 , and E n, R n, S n are irreducible over â.,š, for n=2 ^q m, q=1,2,3,4,5 , and mâ‰11 odd.

Original language	English
Pages (from-to)	269-280
Number of pages	12
Journal	Journal of the Australian Mathematical Society
Volume	92
Issue number	2
DOIs	https://doi.org/10.1017/S1446788712000195
Publication status	Published - Apr 2012

Access to Document

10.1017/S1446788712000195

Cite this

@article{f234a5256df84d81b9f67a7c6f7edb7f,

title = "Cauchy{"}mirimanoff and related polynomials",

abstract = "Abstract In 1903 Mirimanoff conjectured that Cauchy{"}Mirimanoff polynomials E n are irreducible over {\^a}.,{\v s} for odd prime n. Polynomials R n, S n, T n are introduced, closely related to E n. It is proved that R m, S m, T m are irreducible over {\^a}.,{\v s} for odd m{\^a}‰13 , and E n, R n, S n are irreducible over {\^a}.,{\v s}, for n=2 q m, q=1,2,3,4,5 , and m{\^a}‰11 odd.",

keywords = "Cauchy{"}Mirimanoff polynomial, Fermats last theorem, irreducible polynomials",

author = "Nanninga, {Paul M.}",

year = "2012",

month = apr,

doi = "10.1017/S1446788712000195",

language = "English",

volume = "92",

pages = "269--280",

journal = "Journal of the Australian Mathematical Society",

issn = "1446-7887",

publisher = "Cambridge University Press",

number = "2",

}

TY - JOUR

T1 - Cauchy"mirimanoff and related polynomials

AU - Nanninga, Paul M.

PY - 2012/4

Y1 - 2012/4

N2 - Abstract In 1903 Mirimanoff conjectured that Cauchy"Mirimanoff polynomials E n are irreducible over â.,š for odd prime n. Polynomials R n, S n, T n are introduced, closely related to E n. It is proved that R m, S m, T m are irreducible over â.,š for odd mâ‰13 , and E n, R n, S n are irreducible over â.,š, for n=2 q m, q=1,2,3,4,5 , and mâ‰11 odd.

AB - Abstract In 1903 Mirimanoff conjectured that Cauchy"Mirimanoff polynomials E n are irreducible over â.,š for odd prime n. Polynomials R n, S n, T n are introduced, closely related to E n. It is proved that R m, S m, T m are irreducible over â.,š for odd mâ‰13 , and E n, R n, S n are irreducible over â.,š, for n=2 q m, q=1,2,3,4,5 , and mâ‰11 odd.

KW - Cauchy"Mirimanoff polynomial

KW - Fermats last theorem

KW - irreducible polynomials

UR - http://www.scopus.com/inward/record.url?scp=84870185764&partnerID=8YFLogxK

U2 - 10.1017/S1446788712000195

DO - 10.1017/S1446788712000195

M3 - Article

SN - 1446-7887

VL - 92

SP - 269

EP - 280

JO - Journal of the Australian Mathematical Society

JF - Journal of the Australian Mathematical Society

IS - 2

ER -

Cauchy"mirimanoff and related polynomials

Abstract

Access to Document

Other files and links

Fingerprint

Cite this