2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/73392In this article we will show that there are infinitely many symmetric, integral 3 x 3 matrices, with zeros on the diagonal, whose eigenvalues are all integral. We will do this by proving that the rational points on a certain non-Kummer, singular K3 surface are dense. We will also compute the entire Neron-Severi group of this surface and find all low degree curves on it.21 pages, Latex. Changed some typos, definition 5.5, part of the proof of proposition 6.1, and added a reference. Submitted a version with a few more changes suggested by a referee to the Canadian Mathematical BulletinAlgebraic GeometryNumber Theory14J28; 14G05; 14C22text