Problem #PRU-58299

Problems Calculus Real numbers Integer and fractional parts. Archimedean property Methods Pigeonhole principle Pigeonhole principle (angles and lengths)
 13–15  3.0

Problem

Suppose that \(n \geq 3\). Are there n points that do not lie on one line, whose pairwise distances are irrational, and the areas of all of the triangles with vertices in them are rational?