28th Eötvös Competition Problems 1924

1.  The positive integers a, b, c are such that there are triangles with sides an, bn, cn for all positive integers n. Show that at least two of a, b, c must be equal. 2.  What is the locus of the point (in the plane), the sum of whose distances to a given point and line is fixed? 3.  Given three points in the plane, how does one construct three distinct