On integral similitude matrices

Volume 115 / 2009

J. Brzeziński, T. Weibull Colloquium Mathematicum 115 (2009), 1-12 MSC: Primary 11C20, 11G05; Secondary 11D25. DOI: 10.4064/cm115-1-1

Abstract

We study integral similitude $3 \times 3$-matrices and those positive integers which occur as products of their row elements, when matrices are symmetric with the same numbers in each row. It turns out that integers for which nontrivial matrices of this type exist define elliptic curves of nonzero rank and are closely related to generalized cubic Fermat equations.

Authors

  • J. BrzezińskiMathematical Sciences
    University of Gothenburg
    SE-41296 Göteborg, Sweden
    e-mail
  • T. WeibullMathematical Sciences
    Chalmers University of Technology
    SE-41296 Göteborg, Sweden
    e-mail

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