Are there eight points on the plane, no three on a line, no four on a circle, with integer pairwise distances?
The analogous question for seven points was posed by Paul Erdős and answered positively by Kreisel, Kurz 2008, who have then asked this question.
In general, problems by Paul Erdős are worth to check if you want to find problems you are asking for here.
Tobias Kreisel, Sascha Kurz, There Are Integral Heptagons, no Three Points on a Line, no Four on a Circle, Discrete & Computational Geometry 39/4 (2008), 786-790.
