ON PERFECT K-RATIONAL CUBOIDS

Research output: Contribution to journalArticle

Abstract

Let (Formula presented.) be an algebraic number field. A cuboid is said to be (Formula presented.)-rational if its edges and face diagonals lie in (Formula presented.). A (Formula presented.)-rational cuboid is said to be perfect if its body diagonal lies in (Formula presented.). The existence of perfect (Formula presented.)-rational cuboids is an unsolved problem. We prove here that there are infinitely many distinct cubic fields (Formula presented.) such that a perfect (Formula presented.)-rational cuboid exists; and that, for every integer (Formula presented.), there is an algebraic number field (Formula presented.) of degree (Formula presented.) such that there exists a perfect (Formula presented.)-rational cuboid.

Original languageEnglish (US)
Pages (from-to)1-7
Number of pages7
JournalBulletin of the Australian Mathematical Society
DOIs
StateAccepted/In press - Oct 4 2017

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Cuboid
Algebraic number Field
Cubic Fields

Keywords

  • cubic field
  • perfect cuboid
  • rational cuboid
  • Riemann–Roch

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

ON PERFECT K-RATIONAL CUBOIDS. / Bremner, Andrew.

In: Bulletin of the Australian Mathematical Society, 04.10.2017, p. 1-7.

Research output: Contribution to journalArticle

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