2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/125222By means of $q$-series, we prove that any natural number is a sum of an even square and two triangular numbers, and that each positive integer is a sum of a triangular number plus $x^2+y^2$ for some integers $x$ and $y$ with $x\not\equiv y (mod 2)$ or $x=y>0$. The paper also contains some other results and open conjectures on mixed sums of squares and triangular numbers.11 pagesNumber TheoryCombinatorics11E25; 05A30; 11B65; 11D85; 11P99text