We study integral similitude 3 × 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm115-1-1,
author = {J. Brzezi\'nski and T. Weibull},
title = {On integral similitude matrices},
journal = {Colloquium Mathematicae},
volume = {116},
year = {2009},
pages = {1-12},
zbl = {1177.11026},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm115-1-1}
}
J. Brzeziński; T. Weibull. On integral similitude matrices. Colloquium Mathematicae, Tome 116 (2009) pp. 1-12. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm115-1-1/