Let

** m and n **be integers each less than

** 2014**.

Determine the maximum value of

** m^3+n^3** fulfilling the equation

** (n^2 - mn - m^2)^2 = 1**

Another problem from the CBC website, this one submitted by Prof. Peter Rosenthal of the Mathematics Department of the University of Toronto:

This is a question about a tennis tournament. It's organized so that in each round players are randomly paired. If there is an odd number of players, the extra player sits out the round. Losers are all eliminated from the tournament. The rounds continue in the same way until there is only one person remaining, who becomes the champion. The question is: If there are X people who enter the tournament, how many matches will be played in the tournament?