15th Balkan Mathematical Olympiad Problems 1998

15th Balkan Mathematical Olympiad Problems 1998A1.  How many different integers can be written as [n2/1998] for n = 1, 2, ... , 1997? A2.  xi are distinct positive reals satisfying x1 < x2 < ... < x2n+1. Show that x1 - x2 + x3 - x4 + ... - x2n + x2n+1 < (x1n - x2n + ... - x2nn + x2n+1n)1/n.