On perfect k-rational cuboids

Andrew Bremner

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


Let K be an algebraic number field. A cuboid is said to be K-rational if its edges and face diagonals lie in K. A K-rational cuboid is said to be perfect if its body diagonal lies in K. The existence of perfect Q-rational cuboids is an unsolved problem. We prove here that there are infinitely many distinct cubic fields K such that a perfect K-rational cuboid exists; and that, for every integer n≥ 2, there is an algebraic number field K of degree n such that there exists a perfect K-rational cuboid.

Original languageEnglish (US)
Pages (from-to)26-32
Number of pages7
JournalBulletin of the Australian Mathematical Society
Issue number1
StatePublished - Feb 1 2018


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

ASJC Scopus subject areas

  • General Mathematics


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