10th Iberoamerican Mathematical Olympiad Problems 1995

A1.  Find all possible values for the sum of the digits of a square. A2.  n > 1. Find all solutions in real numbers x1, x2, ... , xn+1 all at least 1 such that: (1) x11/2 + x21/3 + x31/4 + ... + xn1/(n+1) = n xn+11/2; and (2) (x1 + x2 + ... + xn)/n = xn+1.