Problem #30
Respect My Authoritah!
The wizard Cartman decides to color a torus with colors. Let the minimum number of colors required to color the n-holed torus be m(n). He has a cube of iron. He asks the blacksmith token to cut it (as in a laser plane is passing through the cube) n times. Let the number of different parts of the cube generated be x(n). But he loves to work with prime numbers and so wants x(n)-k and x(n)+k to be prime. Let the smallest k required to accomplish it be f(n). Your task is to find out \sum_{n=2}^{15}[(m(n)*f(n))]^n