Rational cuboids and Geron triangles - Mazėtis, Edmundas; Melničenko, Grigorijus (Lietuvos matematikos rinkinys, 2018)
The problem of existence of rational cuboids is considered in the article. Equivalent statements of this problem are obtained which lead to the existence of Heron’s triangles whose lengths are integral squares and satisfy other additional conditions. Also, the connections between Euler bricks and the Heron triangles are obtained, which correspond to additional conditions.