On integral similitude matrices
Volume 115 / 2009
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.
