Problem of the Week

The following  problem appeared in the 2003 Mathematical Competition of the Illinois Chapter of the Mathematical Association of America, where the team of Carl Westine, Rich Bernstein and Jacob Corzine from Bradley University received the highest score among all university teams competing.  Congratulations to all!

What is the smallest positive integer x so that  2¹⁶⁸ divides x²⁰⁰³ + 1?

For the hungrier:  For a given positive integer n, what is the smallest positive integer x so that  2ⁿ divides x²⁰⁰³ + 1 ?

You are visitor number 4104 to this page.
ã2003 Alberto L. Delgado