12th Iberoamerican Mathematical Olympiad Problems 1997

A1.  k ≥ 1 is a real number such that if m is a multiple of n, then [mk] is a multiple of [nk]. Show that k is an integer. A2.  I is the incenter of the triangle ABC. A circle with center I meets the side BC at D and P, with D nearer to B. Similarly, it meets the side CA at E and Q, with E nearer to C, and it meets AB at F and R, with F nearer to A. The